How to find the perimeter of a triangle - ISEE Lower Level Quantitative Reasoning
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The triangle below has a perimeter of 
. The lengths of two sides are shown below.
What is the length of the third side?
The triangle below has a perimeter of
What is the length of the third side?
Remember, the perimeter of a triangle is the sum of its three sides. First, sum up the two side lengths that we are given in the question:
To find the third side, subtract the sides we know from the total perimeter:
Remember, the perimeter of a triangle is the sum of its three sides. First, sum up the two side lengths that we are given in the question:
To find the third side, subtract the sides we know from the total perimeter:
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Use the triangle to answer the question.
What is the perimeter of the triangle?
Use the triangle to answer the question.
What is the perimeter of the triangle?
To find the perimeter, add all the sides together.
To find the perimeter, add all the sides together.
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An equilateral triangle has a side length equal to 
.
What is the perimeter of the triangle?
An equilateral triangle has a side length equal to
What is the perimeter of the triangle?
Because it is an equilateral triangle, all sides have the same length 
.
The perimeter is the sum of the length of the sides.
Because it is an equilateral triangle, all sides have the same length
The perimeter is the sum of the length of the sides.
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An equilateral triangle has a perimeter of 42 cm. What is the length of one of its sides?
An equilateral triangle has a perimeter of 42 cm. What is the length of one of its sides?
By definition, an equilateral triangle is a triangle with three equal sides. That is, the length of each side of the triangle is going to be the same.
In this problem, we know that the perimeter (the sum of all the lengths) is 42 cm.
Side 1 + Side 2 + Side 3 = 42 cm.
Since the sides are equal, we can write the following equation. 
one side of the triangle
To find the length of one side of the triangle, we would then divide 3 from both sides.
Remember that 
is the same as 
By definition, an equilateral triangle is a triangle with three equal sides. That is, the length of each side of the triangle is going to be the same.
In this problem, we know that the perimeter (the sum of all the lengths) is 42 cm.
Side 1 + Side 2 + Side 3 = 42 cm.
Since the sides are equal, we can write the following equation.
To find the length of one side of the triangle, we would then divide 3 from both sides.
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Figure not drawn to scale
The perimeter of isosceles triangle 
is 
.
If 
and 
are equal to each other and 
is 
, what is the length of 
?
Figure not drawn to scale
The perimeter of isosceles triangle
If
The perimeter of the triangle is equal to the sum of the lengths of all the sides.
Because the triangle is an isosceles triangle, the triangle has two equal sides, which we know are 
and 
.
Since 
is the same as 
, we can say: 
.
We now solve for 
:
Subtract 
from both sides
Divide both sides by 
The perimeter of the triangle is equal to the sum of the lengths of all the sides.
Because the triangle is an isosceles triangle, the triangle has two equal sides, which we know are
Since
We now solve for
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If an equilateral triangle has sidelengths of 3 inches, what is the perimeter?
If an equilateral triangle has sidelengths of 3 inches, what is the perimeter?
An equilateral triangle is a speical type of triangle that has three congruent sides; in other words, all sides are the same length.
Therefore the perimeter for an equilateral triangle can be written as 
.
Plug in the sidelength given in the question to find the perimeter:
An equilateral triangle is a speical type of triangle that has three congruent sides; in other words, all sides are the same length.
Therefore the perimeter for an equilateral triangle can be written as
Plug in the sidelength given in the question to find the perimeter:
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An equilateral triangle has a perimeter of 
. How long is each side?
An equilateral triangle has a perimeter of
An equilateral triangle has three congruent sides, i.e. the sides are all the same length.
The perimeter of an equilateral triangle is given by 
.
Thus, 
; then divide each side by three to get 
.
An equilateral triangle has three congruent sides, i.e. the sides are all the same length.
The perimeter of an equilateral triangle is given by
Thus,
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What is the name of the longest side of a right triangle?
What is the name of the longest side of a right triangle?
The hypotenuse is the longest side of a triangle with a right angle.
All the other terms refer to something else. Obtuse refers to an angle over 90 degrees. Length is too general of a term, and refers to the measurement of any given side. Equilateral refers to a triangle in which all angles and side are of equal measurement. Base refers to the side that is perpendicular to the measure of the height, meaning that it will be one of the shorter sides.
The hypotenuse is the longest side of a triangle with a right angle.
All the other terms refer to something else. Obtuse refers to an angle over 90 degrees. Length is too general of a term, and refers to the measurement of any given side. Equilateral refers to a triangle in which all angles and side are of equal measurement. Base refers to the side that is perpendicular to the measure of the height, meaning that it will be one of the shorter sides.
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In an isosceles triangle, two side are 4 feet long. Which of the following is NOT a possible length of the third side?
In an isosceles triangle, two side are 4 feet long. Which of the following is NOT a possible length of the third side?
For triangles, it is impossible for a third side to be equal to or greater than the sum of the two other sides.
Given that the sum of the two sides of this triangle is 8, it is impossible for the third side to be equal to 8 feet.
For triangles, it is impossible for a third side to be equal to or greater than the sum of the two other sides.
Given that the sum of the two sides of this triangle is 8, it is impossible for the third side to be equal to 8 feet.
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What is the perimeter of an equilateral triangle for which each side is equal to 4.5?
What is the perimeter of an equilateral triangle for which each side is equal to 4.5?
The perimeter is equal to the sum of the sides of the shape. For an equilateral, all sides are equal. This allows us to simply multiply the given length by 3.
The perimeter is equal to the sum of the sides of the shape. For an equilateral, all sides are equal. This allows us to simply multiply the given length by 3.
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In an equilateral triangle, the perimeter is 42. What is the length of 1 side?
In an equilateral triangle, the perimeter is 42. What is the length of 1 side?
In an equilateral triangle, all 3 sides are equal to one another. Therefore, if the perimeter is 42, the length of 1 side will be equal to 42 divided by 3. This results in 14, which is therefore the correct answer.
In an equilateral triangle, all 3 sides are equal to one another. Therefore, if the perimeter is 42, the length of 1 side will be equal to 42 divided by 3. This results in 14, which is therefore the correct answer.
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In an equilateral triangle, the value of one side is equal to 
. If the perimeter is equal to 18, what is the value of x?
In an equilateral triangle, the value of one side is equal to
The perimeter of an equilateral triangle will be 3 multiplied by one side.
Therefore, the following equation would apply:
Applying the distributive property, the following equation results:
Next, we subtract 12 from each side.
Divide both sides by 3.
The perimeter of an equilateral triangle will be 3 multiplied by one side.
Therefore, the following equation would apply:
Applying the distributive property, the following equation results:
Next, we subtract 12 from each side.
Divide both sides by 3.
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If the side of an equilateral triangle is equal to 
and the perimeter is equal to 18, what is the value of 
?
If the side of an equilateral triangle is equal to
The three sides must sum to 18:
Combine like terms on the left:
Divide both sides by 9:
The three sides must sum to 18:
Combine like terms on the left:
Divide both sides by 9:
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If the perimeter of a triangle is equal to 
inches, and its sides are equal to 
, 
, and 
, what is the length of the longest side (in inches)?
If the perimeter of a triangle is equal to
If the perimeter of a triangle is equal to 
inches, and its sides are equal to 
, 
, and 
, the following equation can be used to determine the value of 
:
Divide each side of the equation by 
.
Given that the longest side of the triangle is equal to 
, the longest side is 
. Therefore, 
is the correct answer.
If the perimeter of a triangle is equal to
Divide each side of the equation by
Given that the longest side of the triangle is equal to
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If the sides of a triangle are equal to 5, 6, and 2x, what is the value of x if the perimeter is 23?
If the sides of a triangle are equal to 5, 6, and 2x, what is the value of x if the perimeter is 23?
The perimeter of a triangle is equal to the sum of its sides. Given that the sides are equal to 5, 6, and 2x, and the perimeter is 23, the appropriate equation to use would be:
(Subtract 11 from each side of the equation.)
(Divide each side of the equation by 2.)
The perimeter of a triangle is equal to the sum of its sides. Given that the sides are equal to 5, 6, and 2x, and the perimeter is 23, the appropriate equation to use would be:
(Subtract 11 from each side of the equation.)
(Divide each side of the equation by 2.)
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If two sides of a triangle measure 
inches and 
inches, which of the following is NOT a possible length (in inches) of the third side?
If two sides of a triangle measure
In a triangle, the length of a third side cannot equal or exceed the sum of the other two sides. The sum of the other two sides is equal to 
. Therefore, the third side cannot be 
inches or greater. Thus, since 
is greater than 
, that cannot be the length of the third side. Thus, 
is the correct answer.
In a triangle, the length of a third side cannot equal or exceed the sum of the other two sides. The sum of the other two sides is equal to
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The sides of a triangle are equal to 
inches, 
foot, and 
inches. What is the perimeter of the triangle in inches?
The sides of a triangle are equal to
The perimeter of a triangle is equal to the sum of its sides.
If the sides of a triangle are equal to 
inches, 
foot, and 
inches, the first step is convert all the sides to inches. This results in:
Therefore, 
is the correct answer.
The perimeter of a triangle is equal to the sum of its sides.
If the sides of a triangle are equal to
Therefore,
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An equilateral triangle has a base of 
. What is the perimeter?
An equilateral triangle has a base of
An equilateral triangle has three equal sides so the side lengths of this triangle are 
and 
.
The perimeter is the total of the three sides so the answer is,
.
An equilateral triangle has three equal sides so the side lengths of this triangle are
The perimeter is the total of the three sides so the answer is,
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If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its perimeter?
If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its perimeter?
If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its perimeter?
Recall that to find perimeter, we simply need to add up the lengths of all the sides.
So our answer must be 24 inches
If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its perimeter?
Recall that to find perimeter, we simply need to add up the lengths of all the sides.
So our answer must be 24 inches
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An isosceles triangle measures 
inches along its two equal sides, and 
inches along its third side. What is the perimeter of the triangle?
An isosceles triangle measures
To find the perimeter of any object, simply add the length of each side together. The best answer is:
To find the perimeter of any object, simply add the length of each side together. The best answer is:
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