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SSAT Upper Level Math : Properties of Triangles

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Example Questions

Example Question #2 : Equilateral Triangles

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

Possible Answers:

$33\:m$

$66\:m$

$56\:m$

$49.5\:m$

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 : Equilateral Triangles

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 : Equilateral Triangles

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 #5 : Equilateral Triangles

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 #6 : Equilateral Triangles

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 #7 : Equilateral Triangles

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

Possible Answers:

8d+6

d+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 #1671 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

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

The sum of their side lengths

Their color

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 #4 : Equilateral Triangles

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

Possible Answers:

The correct answer is not among the other choices.

$768 \sqrt{2}$

$3,072\sqrt{3}$

$768 \sqrt{3}$

$3,072\sqrt{2}$

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 : How To Find The Area Of An Equilateral Triangle

Equilateral

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

Possible Answers:

1,024

$512 \sqrt{3}$

The correct answer is not among the other responses.

$512 \sqrt{6}$

$512 \sqrt{2}$

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,

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

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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Example Question #733 : Ssat Upper Level Quantitative (Math)

The perimeter of an equilateral triangle is $30\sqrt{6}$ . Give its area.

Possible Answers:

$75\sqrt{3}$

$150\sqrt{3}$

$150\sqrt{6}$

$75\sqrt{6}$

$150\sqrt{2}$

Correct answer:

$150\sqrt{3}$

Explanation:

An equilateral triangle with perimeter $30\sqrt{6}$ has three congruent sides of length

$s = 30\sqrt{6}\div 3 = 10\sqrt{6}$

The area of this triangle is

$A = \frac{s^{2}\sqrt{3}}{4} = \frac{ \left ( 10\sqrt{6} \right )^{2}\sqrt{3}}{4} = \frac{100 \cdot 6 \cdot \sqrt{3}}{4} = 150\sqrt{3}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Properties of Triangles

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #2 : Equilateral Triangles

Example Question #3 : Equilateral Triangles

Example Question #4 : Equilateral Triangles

Example Question #5 : Equilateral Triangles

Example Question #6 : Equilateral Triangles

Example Question #7 : Equilateral Triangles

Example Question #1671 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Example Question #4 : Equilateral Triangles

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

Example Question #733 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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