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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Height Of A Triangle

The length of a side of an equilateral triangle is feet. In feet, what is the height of this triangle?

Possible Answers:

$7\sqrt3$

$14\sqrt3$

Correct answer:

$7\sqrt3$

Explanation:

The given equilateral should look similar:

Triangle

Because the height of an equilateral triangle always cuts a side length in half, figuring out the height becomes a matter of applying the Pythagorean Theorem.

$\text{height}^2+7^2=14^2$

$\text{height}^2=147$

$\text{height}=7\sqrt3$

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Example Question #3 : How To Find The Height Of A Triangle

The length of a side of an equilateral triangle is centimeters. In centimeters, what is the length of the height of this triangle?

Possible Answers:

$5\sqrt3$

$10\sqrt3$

Correct answer:

$5\sqrt3$

Explanation:

Draw out the equilateral triangle:

Triangle

Since the height of an equilateral triangle will always cut one of the sides in half, find the height using the Pythagorean Theorem.

$\text{height}^2+5^2=10^2$

$\text{height}^2=75$

$\text{height}=5\sqrt3$

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Example Question #74 : Properties Of Triangles

The length of a side of an equilateral triangle is . Find the length of the height of this triangle.

Possible Answers:

$\sqrt3$

$\text{Cannot determine with the given information}$

$x\sqrt3$

Correct answer:

$x\sqrt3$

Explanation:

Draw out and label the triangle.

Triangle

Even though you are given exponents for the lengths of this triangle, use the Pythagorean Theorem to solve it. The height of an equilateral triangle will always cut one of its bases in half.

$\text{height}^2+x^2=(2x)^2$

$\text{height}^2=3x^2$

$\text{height}=x\sqrt3$

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Example Question #74 : Properties Of Triangles

Find the height of an equilateral triangle that has side lengths of 12r .

Possible Answers:

$6\sqrt3$

$r\sqrt3$

$6r\sqrt3$

$12r\sqrt3$

Correct answer:

$6r\sqrt3$

Explanation:

Draw out and label the triangle.

Triangle

Since the height of an equilateral triangle will always cut its base in half, use the Pythagorean Theorem to find the height.

$\text{height}^2+(6r)^2=(12r)^2$

$\text{height}^2=108r^2$

$\text{height}=6r\sqrt3$

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Example Question #76 : Properties Of Triangles

Find the height of an equilateral triangle that has a side length of 20z .

Possible Answers:

$10\sqrt3$

$10z\sqrt3$

$z\sqrt3$

$20z\sqrt3$

Correct answer:

$10z\sqrt3$

Explanation:

Draw and label this triangle:

Triangle

Since the height of an equilateral triangle always cuts its base in half, use the Pythagorean Theorem to find the height of the triangle.

$\text{height}^2+(10z)^2=(20z)^2$

$\text{height}^2=300z^2$

$\text{height}=10z\sqrt3$

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Example Question #81 : Properties Of Triangles

Find the height of an equilateral triangle, in yards, that has side lengths of yards.

Possible Answers:

$28\sqrt3$

$14\sqrt3$

Correct answer:

$14\sqrt3$

Explanation:

Triangle

Since the height of an equilateral triangle cuts the base in half, use the Pythagorean Theorem to find the height.

$\text{height}^2+14^2=28^2$

$\tet{height}^2=588$

$\text{height}=14\sqrt3$

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Example Question #6 : How To Find The Height Of A Triangle

An equilateral triangle has sides of length . Find the measure of the height for this triangle.

Possible Answers:

$3\sqrt3$

$\sqrt3$

$3\sqrt2$

Correct answer:

$3\sqrt3$

Explanation:

Triangle

The height of an equilateral triangle will always cut the side it intersects in half. Now, this is just a matter of applying the Pythagorean Theorem.

$6^2=3^2+\text{height}^2$

$\text{height}^2=27$

$\text{height}=3\sqrt3$

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Example Question #521 : Geometry

The length of a side in a equilateral triangle is f-9 . Find the perimeter of this triangle.

Possible Answers:

3f-9

3f+9

3f-27

Correct answer:

3f-27

Explanation:

Since an equilateral triangle has side lengths that are all the same, multiply the length of one side by to find the perimeter.

3(f-9)=3f-27

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Example Question #522 : Geometry

The length of one side of an equilateral triangle is 2g-1 . What is the perimeter for this triangle?

Possible Answers:

6g-3

2g-3

6g-1

Correct answer:

6g-3

Explanation:

Since an equilateral triangle has sides that are all equal, multiply the length of one side by to find the perimeter.

3(2g-1)=6g-3

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Example Question #741 : Ssat Upper Level Quantitative (Math)

The length of one side of an equilateral triangle is 5h+8 . What is the perimeter for this triangle?

Possible Answers:

15h+24

5h+24

15h+8

Correct answer:

15h+24

Explanation:

Since an equilateral triangle has sides that are all equal, multiply the length of one side by to find the perimeter.

3(5h+8)=15h+24

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Height Of A Triangle

Example Question #3 : How To Find The Height Of A Triangle

Example Question #74 : Properties Of Triangles

Example Question #74 : Properties Of Triangles

Example Question #76 : Properties Of Triangles

Example Question #81 : Properties Of Triangles

Example Question #6 : How To Find The Height Of A Triangle

Example Question #521 : Geometry

Example Question #522 : Geometry

Example Question #741 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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