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SSAT Upper Level Math : Equilateral Triangles

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Example Questions

Example Question #1 : Equilateral Triangles

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

Possible Answers:

800 $\displaystyle 800$ units

400 $\displaystyle 400$ units

300 $\displaystyle 300$ units

600 $\displaystyle 600$ units

Correct answer:

800 $\displaystyle 800$ 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.

$2400\div3=800$ $\displaystyle 2400\div3=800$

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

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

Possible Answers:

$33\:m$ $\displaystyle 33\:m$

$56\:m$ $\displaystyle 56\:m$

$49.5\:m$ $\displaystyle 49.5\:m$

$66\:m$ $\displaystyle 66\:m$

Correct answer:

$33\:m$ $\displaystyle 33\:m$

Explanation:

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

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

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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 36x $\displaystyle 36x$ . What is the length of a side of this triangle?

Possible Answers:

12x $\displaystyle 12x$

24x $\displaystyle 24x$

$\displaystyle 12$

$\displaystyle 24$

Correct answer:

12x $\displaystyle 12x$

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.

$36x\div3=12x$ $\displaystyle 36x\div3=12x$

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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 120t $\displaystyle 120t$ . What is the length of one side of the triangle?

Possible Answers:

20t $\displaystyle 20t$

40t $\displaystyle 40t$

30t $\displaystyle 30t$

$\displaystyle 40$

Correct answer:

40t $\displaystyle 40t$

Explanation:

Since an equilateral triangle has sides that are all the same, divide the perimeter by $\displaystyle 3$ to get the length of each side.

$120t\div3=40t$ $\displaystyle 120t\div3=40t$

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Example Question #2 : Equilateral Triangles

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

Possible Answers:

$\displaystyle 26$

$\displaystyle 17$

$\displaystyle 8$

$\displaystyle 13$

Correct answer:

$\displaystyle 13$

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.

$39\div3=13$ $\displaystyle 39\div3=13$

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Example Question #3 : Equilateral Triangles

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

Possible Answers:

75c+4 $\displaystyle 75c+4$

25c+12 $\displaystyle 25c+12$

$\displaystyle 79$

25c+4 $\displaystyle 25c+4$

Correct answer:

25c+4 $\displaystyle 25c+4$

Explanation:

Since an equilateral triangle has three equal sides, divide the perimeter by $\displaystyle 3$ to find the length of each side.

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

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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 24d-18 $\displaystyle 24d-18$ . What is the length of one side of this triangle?

Possible Answers:

8d+6 $\displaystyle 8d+6$

$\displaystyle 2$

8d-6 $\displaystyle 8d-6$

d+6 $\displaystyle d+6$

Correct answer:

8d-6 $\displaystyle 8d-6$

Explanation:

Since an equilateral triangle has three equal sides, divide the perimeter by $\displaystyle 3$ to find the length of one side.

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

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Example Question #52 : Geometry

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

Possible Answers:

The number of side lengths

The length of their sides

The sum of their angle measurements

Their color

The sum of their side lengths

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 $\displaystyle 3$ equal sides, but a scalene triangle can have all different side lengths.

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Example Question #1 : Equilateral Triangles

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

Possible Answers:

$3,072\sqrt{2}$ $\displaystyle 3,072\sqrt{2}$

$768 \sqrt{2}$ $\displaystyle 768 \sqrt{2}$

The correct answer is not among the other choices.

$768 \sqrt{3}$ $\displaystyle 768 \sqrt{3}$

$3,072\sqrt{3}$ $\displaystyle 3,072\sqrt{3}$

Correct answer:

$768 \sqrt{3}$ $\displaystyle 768 \sqrt{3}$

Explanation:

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

Equilateral

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

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

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

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

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

Equilateral

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

Possible Answers:

1,024 $\displaystyle 1,024$

$512 \sqrt{3}$ $\displaystyle 512 \sqrt{3}$

The correct answer is not among the other responses.

$512 \sqrt{6}$ $\displaystyle 512 \sqrt{6}$

$512 \sqrt{2}$ $\displaystyle 512 \sqrt{2}$

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,

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

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

The area of this triangle is half the product of the base $\displaystyle BC$ and the height $\displaystyle AM$ :

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

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

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 #2 : Equilateral Triangles

Example Question #3 : Equilateral Triangles

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

Example Question #52 : Geometry

Example Question #1 : Equilateral Triangles

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

All SSAT Upper Level Math Resources

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