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SSAT Upper Level Math : Equilateral Triangles

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

Example Questions

Example Question #1 : Equilateral Triangles

An equilateral triangle has a perimeter of 2400 units. What is the length of each side?

Possible Answers:

300 units

800 units

400 units

600 units

Correct answer:

800 units

Explanation:

Because an equilateral triangle has three sides that are the same length, divide the given perimeter by 3 to find the length of each side.

$2400\div3=800$

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Example Question #2 : How To Find The Length Of The Side Of An Equilateral Triangle

The perimeter of a equilateral triangle is $99\:m$ . In meters, what is the length of a side of this triangle?

Possible Answers:

$66\:m$

$49.5\:m$

$56\:m$

$33\:m$

Correct answer:

$33\:m$

Explanation:

Since all three sides are equal in an equilateral triangle, we can just divide the perimeter by 3 to find a side length.

$99\:m\div3\:m=33\:m$

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Example Question #3 : How To Find The Length Of The Side Of An Equilateral Triangle

The perimeter of an equilateral triangle is 36x . What is the length of a side of this triangle?

Possible Answers:

12x

24x

Correct answer:

12x

Explanation:

Because all the sides in an equilateral triangle are equal, we can just divide the perimeter by 3 to find the length of a side.

$36x\div3=12x$

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Example Question #4 : How To Find The Length Of The Side Of An Equilateral Triangle

The perimeter of an equilateral triangle is 120t . What is the length of one side of the triangle?

Possible Answers:

20t

40t

30t

Correct answer:

40t

Explanation:

Since an equilateral triangle has sides that are all the same, divide the perimeter by to get the length of each side.

$120t\div3=40t$

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Example Question #1 : How To Find The Length Of The Side Of An Equilateral Triangle

The perimeter of an equilateral triangle is 39 meters. In meters, how long is one side of the triangle?

Possible Answers:

Correct answer:

Explanation:

An equilateral triangle has sides that are the same length. Then, to find the length of one side, you only need to divide the perimeter by 3.

$39\div3=13$

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Example Question #721 : Ssat Upper Level Quantitative (Math)

The perimeter of an equilateral triangle is 75c+12 . What is the length of one side of this triangle?

Possible Answers:

25c+12

25c+4

75c+4

Correct answer:

25c+4

Explanation:

Since an equilateral triangle has three equal sides, divide the perimeter by to find the length of each side.

$\frac{75c+12}{3}=25c+4$

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Example Question #2 : How To Find The Length Of The Side Of An Equilateral Triangle

The perimeter of an equilateral triangle is 24d-18 . What is the length of one side of this triangle?

Possible Answers:

d+6

8d+6

8d-6

Correct answer:

8d-6

Explanation:

Since an equilateral triangle has three equal sides, divide the perimeter by to find the length of one side.

$\frac{24d-18}{3}=8d-6$

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Example Question #1 : How To Find The Length Of The Side Of An Equilateral Triangle

What is the difference between an equilateral triangle and a scalene triangle?

Possible Answers:

The sum of their side lengths

The number of side lengths

The sum of their angle measurements

Their color

The length of their sides

Correct answer:

The length of their sides

Explanation:

Of the choices listed, the main difference between an equilateral triangle and a scalene triangle is their side lengths. An equilateral triangle has to have equal sides, but a scalene triangle can have all different side lengths.

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Example Question #9 : Equilateral Triangles

An equilateral triangle is circumscribed about a circle of radius 16. Give the area of the triangle.

Possible Answers:

$768 \sqrt{2}$

$3,072\sqrt{3}$

$3,072\sqrt{2}$

The correct answer is not among the other choices.

$768 \sqrt{3}$

Correct answer:

$768 \sqrt{3}$

Explanation:

The circle and triangle referenced are below, along with a radius to one side and a segment to one vertex:

Equilateral

$\Delta ABO$ is a 30-60-90 triangle, so

$AB = OB \cdot \sqrt{3} = 16 \sqrt{3}$

$\overline{AB}$ is one-half of a side of the triangle, so the sidelength is $32\sqrt{3}$ . The area of the triangle is

$A = \frac{s^{2} \sqrt{3}}{4} = \frac{(32\sqrt{3})^{2} \sqrt{3}}{4} = \frac{1,024 \cdot 3 \cdot \sqrt{3}}{4}= 768 \sqrt{3}$

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Example Question #1 : Equilateral Triangles

Equilateral

In the above diagram, $\Delta ABC$ is equilateral. Give its area.

Possible Answers:

The correct answer is not among the other responses.

$512 \sqrt{6}$

$512 \sqrt{2}$

1,024

$512 \sqrt{3}$

Correct answer:

The correct answer is not among the other responses.

Explanation:

The interior angles of an equilateral triangle all measure 60 degrees, so, by the 30-60-90 Theorem,

$BM = \frac{AM}{\sqrt{3}} = \frac{32}{\sqrt{3}}$

Also, is the midpoint of $\overline{BC}$ , so $BC = 2 \cdot BM = \frac{64}{\sqrt{3}}$ ; this is the base.

The area of this triangle is half the product of the base and the height :

$A= \frac{1}{2} \cdot 32 \cdot \frac{64}{\sqrt{3}}= \frac{1,024}{\sqrt{3}} = \frac{1,024\cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}= \frac{1,024 \sqrt{3}}{3}$

This answer is not among the given choices.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Equilateral Triangles

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Equilateral Triangles

Example Question #2 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #3 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #4 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #1 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #721 : Ssat Upper Level Quantitative (Math)

Example Question #2 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #1 : How To Find The Length Of The Side Of An Equilateral Triangle

Example Question #9 : Equilateral Triangles

Example Question #1 : Equilateral Triangles

All SSAT Upper Level Math Resources

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