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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #24 : Triangles

Find the perimeter of an equilateral triangle with a base of length 34in.

Possible Answers:

$68\text{in}$

$102\text{in}$

$94\text{in}$

$51\text{in}$

$76\text{in}$

Correct answer:

$102\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 34in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 34in.

Knowing this, we can substitute into the formula. We get

$P = 34\text{in} + 34\text{in} +34\text{in}$

$P = 102\text{in}$

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Example Question #21 : Triangles

Find the perimeter of a triangle that has a base of 16in.

Possible Answers:

$24\text{in}$

$32\text{in}$

$108\text{in}$

$48\text{in}$

$128\text{in}$

Correct answer:

$48\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 16in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 16in.

Knowing this, we will substitute into the formula. We get

$P = 16\text{in} + 16\text{in} + 16\text{in}$

$P = 48\text{in}$

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Example Question #26 : Triangles

Use the following triangle to answer the question:

Triangle7

Find the perimeter.

Possible Answers:

$32\text{cm}$

$24\text{cm}$

$18\text{cm}$

$48\text{cm}$

$14\text{cm}$

Correct answer:

$18\text{cm}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle,

Triangle7

we can see it has sides with length 8cm, 4cm, and 6cm. Knowing this, we can substitute into the formula. We get

$P = 8\text{cm} +4\text{cm} + 6\text{cm}$

$P=18\text{cm}$

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Example Question #21 : Geometry

The perimeter of an equilateral triangle is 39cm. Find the length of one side.

Possible Answers:

$12\text{cm}$

$\text{There is not enough information to answer the question.}$

$13\text{cm}$

$14\text{cm}$

$11\text{cm}$

Correct answer:

$13\text{cm}$

Explanation:

To find the perimeter of an equilateral triangle, we use this formula

P = 3a

where a is the length of one side. An equilateral triangle has 3 equal sides. That is why we multiply the length of one side by 3. To find the length of one side, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 39cm. So, we can substitute. We get

$39\text{cm} = 3a$

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

$13\text{cm} = a$

$a=13\text{cm}$

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

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Example Question #28 : Triangles

Find the perimeter of an equilateral triangle with a base of 14in.

Possible Answers:

$48\text{in}$

$28\text{in}$

$42\text{in}$

$\text{There is not enough information to solve the problem.}$

$36\text{in}$

Correct answer:

$42\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 14in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 14in. So, we can substitute.

$P = 14\text{in} + 14\text{in} + 14\text{in}$

$P = 42\text{in}$

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Example Question #31 : Plane Geometry

Find the perimeter of an equilateral triangle with a side of length 7in.

Possible Answers:

$29\text{in}$

$14\text{in}$

$21\text{in}$

$24\text{in}$

$28\text{in}$

Correct answer:

$21\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the equilateral triangle has one side of length 7in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 7in. So, we can substitute. We get

$P = 7\text{in} + 7\text{in} + 7\text{in}$

$P = 21\text{in}$

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Example Question #32 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of 13in.

Possible Answers:

$48\text{in}$

$27\text{in}$

$169\text{in}$

$36\text{in}$

$39\text{in}$

Correct answer:

$39\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 13in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 13in. So, we get

$P = 13\text{in} + 13\text{in} + 13\text{in}$

$P = 39\text{in}$

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Example Question #33 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of length 9in.

Possible Answers:

$27\text{in}$

$18\text{in}$

$\text{There is not enough information to solve the problem.}$

$32\text{in}$

$36\text{in}$

Correct answer:

$27\text{in}$

Explanation:

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

P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle has a length of 9in. Because it is an equilateral triangle, all lengths are the same. Therefore, all lengths are 9in.

Knowing this, we can substitute into the formula. We get

$P = 9\text{in} +9\text{in} +9\text{in}$

$P = 27\text{in}$

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Example Question #1221 : Concepts

A triangle has a base of $\small 43$ and an area of $\small 2042.5$ . What is the height?

Possible Answers:

$\small 95$

$\small 48$

$\small 190$

$\small 47$

$\small 93$

Correct answer:

$\small 95$

Explanation:

The area of a triangle is found by multiplying the base by the height and dividing by two:

$\small \frac{b\cdot h}{2}$

In this problem we are given the base, which is $\small 43$ , and the area, which is $\small 2042.5$ . First we write an equation using $\small h$ as our variable.

$\small \frac{43\cdot h}{2}=2042.5$

To solve this equation, first multply both sides by $\small 2$ , becuase multiplication is the opposite of division and therefore allows us to eliminate the $\small 2$ .

The left-hand side simplifies to:

$\small \frac{43\cdot h}{2}\cdot 2=43\cdot h$

The right-hand side simplifies to:

$\small 2042.5\cdot 2=4085$

So our equation is now:

$\small \small 43\cdot h=4085$

Next we divide both sides by $\small \small 43$ , because division is the opposite of multiplication, so it allows us to isolate the variable by eliminating $\small \small 43$ .

$\small \frac{43\cdot h}{43}= h$

$\small \frac{4085}{43}=95$

$\small h=95$

So the height of the triangle is $\small 95$ .

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Example Question #1851 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Triangle

Note: Figure NOT drawn to scale.

The above triangle has area 36 square inches. If $x = 4.5 \textrm{ in}$ , then what is ?

Possible Answers:

$y = 20 \textrm{ in}$

$y = 32 \textrm{ in}$

$y = 26 \textrm{ in}$

$y = 16 \textrm{ in}$

$y = 24\textrm{ in}$

Correct answer:

$y = 16 \textrm{ in}$

Explanation:

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

$A = \frac{1}{2}xy$ .

Substitute A = 36, x = 4.5 , and solve for .

$\frac{1}{2} \cdot 4.5 \cdot y = 36$

2.25 y = 36

$2.25 y \div 2.25= 36\div 2.25$

$y = 16 \textrm{ in}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #24 : Triangles

Example Question #21 : Triangles

Example Question #26 : Triangles

Example Question #21 : Geometry

Example Question #28 : Triangles

Example Question #31 : Plane Geometry

Example Question #32 : Plane Geometry

Example Question #33 : Plane Geometry

Example Question #1221 : Concepts

Example Question #1851 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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