How to find the length of the side of an equilateral triangle - ISEE Upper Level Quantitative Reasoning

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Question

Which of the following could be the three sidelengths of an equilateral triangle?

Answer

By definition, an equilateral triangle has three sides of equal length. We can identify the equilateral triangle by converting the given sidelengths to the same units and comparing them.

We can eliminate the following by showing that at least two sidelengths differ.

$2 \textrm{ yd, } 84 \textrm{ in, }7\textrm{ ft}$

2 yards = $2 \times 3 = 6$ feet.

Two sides have lengths 6 feet and 7 feet, so we can eliminate this choice.

$1\frac{1}{2} \textrm{ yd, } 50 \textrm{ in, }4\textrm{ ft}$

4 feet = $4 \times 12 = 48$ inches

Two sides have lengths 48 inches and 50 inches, so we can eliminate this choice.

$1\frac{1}{3} \textrm{ yd, } 48 \textrm{ in, }5\textrm{ ft}$

5 feet = $5 \times 12 = 60$ inches

Two sides have lengths 48 inches and 60 inches, so we can eliminate this choice.

$1\frac{2}{3} \textrm{ yd, } 48 \textrm{ in, }4\textrm{ ft}$

$1\frac{2}{3}$ yards = $1\frac{2}{3} \times 3 = 5$ feet

Two sides have lengths 4 feet and 5 feet, so we can eliminate this choice.

$\frac{2}{3} \textrm{ yd, } 24 \textrm{ in, }2\textrm{ ft}$

$\frac{2}{3}$ yards = $\frac{2}{3} \times3 = 2$ feet = $2 \times 12 = 24$ inches

All three sides have the same length, making this the triangle equilateral. This choice is correct.

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Question

For an equilateral triangle, Side A measures and Side B measures . What is the length of Side A?

Answer

First you need to recognize that for an equilateral triangle, all 3 sides have equal lengths.

This means you can set the two values for Side A and Side B equal to one another, since they measure the same length, to solve for .

You now know that , but this is not your answer. The question asked for the length of Side A, so you need to plug 3 into that equation.

So the length of Side A (and Side B for that matter) is 8.

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Question

One angle of an equilateral triangle is 60 degrees. One side of that triangle is 12 centimeters. What are the measures of the two other angles and two other sides?

Answer

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°. Since all sides are congruent, the other two sides both measure 12 centimeters.

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Question

If an equilateral triangle has a perimeter of 18in, what is the length of one side?

Answer

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of any side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side of the triangle, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 18in. So, we will substitute.

$18\text{in} = 3a$

$\frac{18\text{in}}{3} = \frac{3a}{3}$

$6\text{in} = a$

$a=6\text{in}$

Therefore, the length of one side of the equilateral triangle is 6in.

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Question

An equilateral triangle has a perimeter of 39in. Find the length of one side.

Answer

An equilateral triangle has 3 equal sides. So, to find the length of one side, we will use what we know. We know the perimeter of the equilateral triangle is 39in. So, we will look at the formula for perimeter. We get

where a is the length of one side of the triangle. So, to find the length of one side, we will solve for a. Now, as stated before, we know the perimeter of the triangle is 39in. So, we will substitute and solve for a. We get

$39\text{in} = 3a$

$\frac{39\text{in}}{3} = \frac{3a}{3}$

$13\text{in} = a$

$a = 13\text{in}$

Therefore, the length of one side of the equilateral triangle is 13in.

Compare your answer with the correct one above

Question

Which of the following could be the three sidelengths of an equilateral triangle?

Answer

By definition, an equilateral triangle has three sides of equal length. We can identify the equilateral triangle by converting the given sidelengths to the same units and comparing them.

We can eliminate the following by showing that at least two sidelengths differ.

$2 \textrm{ yd, } 84 \textrm{ in, }7\textrm{ ft}$

2 yards = $2 \times 3 = 6$ feet.

Two sides have lengths 6 feet and 7 feet, so we can eliminate this choice.

$1\frac{1}{2} \textrm{ yd, } 50 \textrm{ in, }4\textrm{ ft}$

4 feet = $4 \times 12 = 48$ inches

Two sides have lengths 48 inches and 50 inches, so we can eliminate this choice.

$1\frac{1}{3} \textrm{ yd, } 48 \textrm{ in, }5\textrm{ ft}$

5 feet = $5 \times 12 = 60$ inches

Two sides have lengths 48 inches and 60 inches, so we can eliminate this choice.

$1\frac{2}{3} \textrm{ yd, } 48 \textrm{ in, }4\textrm{ ft}$

$1\frac{2}{3}$ yards = $1\frac{2}{3} \times 3 = 5$ feet

Two sides have lengths 4 feet and 5 feet, so we can eliminate this choice.

$\frac{2}{3} \textrm{ yd, } 24 \textrm{ in, }2\textrm{ ft}$

$\frac{2}{3}$ yards = $\frac{2}{3} \times3 = 2$ feet = $2 \times 12 = 24$ inches

All three sides have the same length, making this the triangle equilateral. This choice is correct.

Compare your answer with the correct one above

Question

For an equilateral triangle, Side A measures and Side B measures . What is the length of Side A?

Answer

First you need to recognize that for an equilateral triangle, all 3 sides have equal lengths.

This means you can set the two values for Side A and Side B equal to one another, since they measure the same length, to solve for .

You now know that , but this is not your answer. The question asked for the length of Side A, so you need to plug 3 into that equation.

So the length of Side A (and Side B for that matter) is 8.

Compare your answer with the correct one above

Question

One angle of an equilateral triangle is 60 degrees. One side of that triangle is 12 centimeters. What are the measures of the two other angles and two other sides?

Answer

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°. Since all sides are congruent, the other two sides both measure 12 centimeters.

Compare your answer with the correct one above

Question

If an equilateral triangle has a perimeter of 18in, what is the length of one side?

Answer

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of any side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side of the triangle, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 18in. So, we will substitute.

$18\text{in} = 3a$

$\frac{18\text{in}}{3} = \frac{3a}{3}$

$6\text{in} = a$

$a=6\text{in}$

Therefore, the length of one side of the equilateral triangle is 6in.

Compare your answer with the correct one above

Question

An equilateral triangle has a perimeter of 39in. Find the length of one side.

Answer

An equilateral triangle has 3 equal sides. So, to find the length of one side, we will use what we know. We know the perimeter of the equilateral triangle is 39in. So, we will look at the formula for perimeter. We get

where a is the length of one side of the triangle. So, to find the length of one side, we will solve for a. Now, as stated before, we know the perimeter of the triangle is 39in. So, we will substitute and solve for a. We get

$39\text{in} = 3a$

$\frac{39\text{in}}{3} = \frac{3a}{3}$

$13\text{in} = a$

$a = 13\text{in}$

Therefore, the length of one side of the equilateral triangle is 13in.

Compare your answer with the correct one above

Question

Which of the following could be the three sidelengths of an equilateral triangle?

Answer

By definition, an equilateral triangle has three sides of equal length. We can identify the equilateral triangle by converting the given sidelengths to the same units and comparing them.

We can eliminate the following by showing that at least two sidelengths differ.

$2 \textrm{ yd, } 84 \textrm{ in, }7\textrm{ ft}$

2 yards = $2 \times 3 = 6$ feet.

Two sides have lengths 6 feet and 7 feet, so we can eliminate this choice.

$1\frac{1}{2} \textrm{ yd, } 50 \textrm{ in, }4\textrm{ ft}$

4 feet = $4 \times 12 = 48$ inches

Two sides have lengths 48 inches and 50 inches, so we can eliminate this choice.

$1\frac{1}{3} \textrm{ yd, } 48 \textrm{ in, }5\textrm{ ft}$

5 feet = $5 \times 12 = 60$ inches

Two sides have lengths 48 inches and 60 inches, so we can eliminate this choice.

$1\frac{2}{3} \textrm{ yd, } 48 \textrm{ in, }4\textrm{ ft}$

$1\frac{2}{3}$ yards = $1\frac{2}{3} \times 3 = 5$ feet

Two sides have lengths 4 feet and 5 feet, so we can eliminate this choice.

$\frac{2}{3} \textrm{ yd, } 24 \textrm{ in, }2\textrm{ ft}$

$\frac{2}{3}$ yards = $\frac{2}{3} \times3 = 2$ feet = $2 \times 12 = 24$ inches

All three sides have the same length, making this the triangle equilateral. This choice is correct.

Compare your answer with the correct one above

Question

For an equilateral triangle, Side A measures and Side B measures . What is the length of Side A?

Answer

First you need to recognize that for an equilateral triangle, all 3 sides have equal lengths.

This means you can set the two values for Side A and Side B equal to one another, since they measure the same length, to solve for .

You now know that , but this is not your answer. The question asked for the length of Side A, so you need to plug 3 into that equation.

So the length of Side A (and Side B for that matter) is 8.

Compare your answer with the correct one above

Question

One angle of an equilateral triangle is 60 degrees. One side of that triangle is 12 centimeters. What are the measures of the two other angles and two other sides?

Answer

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°. Since all sides are congruent, the other two sides both measure 12 centimeters.

Compare your answer with the correct one above

Question

If an equilateral triangle has a perimeter of 18in, what is the length of one side?

Answer

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of any side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side of the triangle, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 18in. So, we will substitute.

$18\text{in} = 3a$

$\frac{18\text{in}}{3} = \frac{3a}{3}$

$6\text{in} = a$

$a=6\text{in}$

Therefore, the length of one side of the equilateral triangle is 6in.

Compare your answer with the correct one above

Question

An equilateral triangle has a perimeter of 39in. Find the length of one side.

Answer

An equilateral triangle has 3 equal sides. So, to find the length of one side, we will use what we know. We know the perimeter of the equilateral triangle is 39in. So, we will look at the formula for perimeter. We get

where a is the length of one side of the triangle. So, to find the length of one side, we will solve for a. Now, as stated before, we know the perimeter of the triangle is 39in. So, we will substitute and solve for a. We get

$39\text{in} = 3a$

$\frac{39\text{in}}{3} = \frac{3a}{3}$

$13\text{in} = a$

$a = 13\text{in}$

Therefore, the length of one side of the equilateral triangle is 13in.

Compare your answer with the correct one above

Question

Which of the following could be the three sidelengths of an equilateral triangle?

Answer

By definition, an equilateral triangle has three sides of equal length. We can identify the equilateral triangle by converting the given sidelengths to the same units and comparing them.

We can eliminate the following by showing that at least two sidelengths differ.

$2 \textrm{ yd, } 84 \textrm{ in, }7\textrm{ ft}$

2 yards = $2 \times 3 = 6$ feet.

Two sides have lengths 6 feet and 7 feet, so we can eliminate this choice.

$1\frac{1}{2} \textrm{ yd, } 50 \textrm{ in, }4\textrm{ ft}$

4 feet = $4 \times 12 = 48$ inches

Two sides have lengths 48 inches and 50 inches, so we can eliminate this choice.

$1\frac{1}{3} \textrm{ yd, } 48 \textrm{ in, }5\textrm{ ft}$

5 feet = $5 \times 12 = 60$ inches

Two sides have lengths 48 inches and 60 inches, so we can eliminate this choice.

$1\frac{2}{3} \textrm{ yd, } 48 \textrm{ in, }4\textrm{ ft}$

$1\frac{2}{3}$ yards = $1\frac{2}{3} \times 3 = 5$ feet

Two sides have lengths 4 feet and 5 feet, so we can eliminate this choice.

$\frac{2}{3} \textrm{ yd, } 24 \textrm{ in, }2\textrm{ ft}$

$\frac{2}{3}$ yards = $\frac{2}{3} \times3 = 2$ feet = $2 \times 12 = 24$ inches

All three sides have the same length, making this the triangle equilateral. This choice is correct.

Compare your answer with the correct one above

Question

For an equilateral triangle, Side A measures and Side B measures . What is the length of Side A?

Answer

First you need to recognize that for an equilateral triangle, all 3 sides have equal lengths.

This means you can set the two values for Side A and Side B equal to one another, since they measure the same length, to solve for .

You now know that , but this is not your answer. The question asked for the length of Side A, so you need to plug 3 into that equation.

So the length of Side A (and Side B for that matter) is 8.

Compare your answer with the correct one above

Question

One angle of an equilateral triangle is 60 degrees. One side of that triangle is 12 centimeters. What are the measures of the two other angles and two other sides?

Answer

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°. Since all sides are congruent, the other two sides both measure 12 centimeters.

Compare your answer with the correct one above

Question

If an equilateral triangle has a perimeter of 18in, what is the length of one side?

Answer

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of any side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side of the triangle, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 18in. So, we will substitute.

$18\text{in} = 3a$

$\frac{18\text{in}}{3} = \frac{3a}{3}$

$6\text{in} = a$

$a=6\text{in}$

Therefore, the length of one side of the equilateral triangle is 6in.

Compare your answer with the correct one above

Question

An equilateral triangle has a perimeter of 39in. Find the length of one side.

Answer

An equilateral triangle has 3 equal sides. So, to find the length of one side, we will use what we know. We know the perimeter of the equilateral triangle is 39in. So, we will look at the formula for perimeter. We get

where a is the length of one side of the triangle. So, to find the length of one side, we will solve for a. Now, as stated before, we know the perimeter of the triangle is 39in. So, we will substitute and solve for a. We get

$39\text{in} = 3a$

$\frac{39\text{in}}{3} = \frac{3a}{3}$

$13\text{in} = a$

$a = 13\text{in}$

Therefore, the length of one side of the equilateral triangle is 13in.

Compare your answer with the correct one above

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