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SSAT Middle Level Math : Triangles

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

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Example Questions

Example Question #1 : Geometry

What is the perimeter of an equilateral triangle with a side length $\displaystyle 4$?

Possible Answers:

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 16$

$\displaystyle 12$

$\displaystyle 20$

Correct answer:

$\displaystyle 12$

Explanation:

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

$\displaystyle P=4+4+4=12$

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Example Question #1 : Triangles

Find the perimeter of a triangle with sides 8cm $\displaystyle 8cm$, 9cm $\displaystyle 9cm$, and 11cm $\displaystyle 11cm$.

Possible Answers:

16cm $\displaystyle 16cm$

28cm $\displaystyle 28cm$

24cm $\displaystyle 24cm$

30cm $\displaystyle 30cm$

19cm $\displaystyle 19cm$

Correct answer:

28cm $\displaystyle 28cm$

Explanation:

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals 9+8+11 $\displaystyle 9+8+11$. Therefore, the answer is 28cm $\displaystyle 28cm$.

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Example Question #2 : Geometry

A right triangle has legs $\displaystyle 9$ feet and $\displaystyle 12$ feet long. What is its perimeter, in inches?

Possible Answers:

$252 \textrm{ in}$ $\displaystyle 252 \textrm{ in}$

$216 \textrm{ in}$ $\displaystyle 216 \textrm{ in}$

$864 \textrm{ in}$ $\displaystyle 864 \textrm{ in}$

$432 \textrm{ in}$ $\displaystyle 432 \textrm{ in}$

$504 \textrm{ in}$ $\displaystyle 504 \textrm{ in}$

Correct answer:

$432 \textrm{ in}$ $\displaystyle 432 \textrm{ in}$

Explanation:

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute $\displaystyle a = 9,b= 12$:

$c = \sqrt{a ^{2} + b^{2} } =\sqrt{9 ^{2} +12^{2} } = \sqrt{81+144} = \sqrt{225} = 15$ $\displaystyle c = \sqrt{a ^{2} + b^{2} } =\sqrt{9 ^{2} +12^{2} } = \sqrt{81+144} = \sqrt{225} = 15$ feet

Its perimeter is $\displaystyle P = 9 + 12 + 15 = 36$ feet. Multiply by 12 to get the perimeter in inches:

$36 \times 12 = 432$ $\displaystyle 36 \times 12 = 432$ inches

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Example Question #1 : Geometry

An equilateral triangle has perimeter 73.5 $\displaystyle 73.5$ centimeters. How long is one side?

Possible Answers:

$24.5 \textrm{ cm}$ $\displaystyle 24.5 \textrm{ cm}$

$29.4 \textrm{ cm}$ $\displaystyle 29.4 \textrm{ cm}$

$36.75 \textrm{ cm}$ $\displaystyle 36.75 \textrm{ cm}$

$18.375 \textrm{ cm}$ $\displaystyle 18.375 \textrm{ cm}$

$14.7 \textrm{ cm} ^{2}$ $\displaystyle 14.7 \textrm{ cm} ^{2}$

Correct answer:

$24.5 \textrm{ cm}$ $\displaystyle 24.5 \textrm{ cm}$

Explanation:

An equilateral triangle has three sides of equal measure, so divide its perimeter by $\displaystyle 3$:

$73.5 \div 3 =24.5 \textrm{ cm}$ $\displaystyle 73.5 \div 3 =24.5 \textrm{ cm}$

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Example Question #261 : Ssat Middle Level Quantitative (Math)

Find the perimeter of an equilateral triangle with a base of 11in.

Possible Answers:

$121\text{in}$ $\displaystyle 121\text{in}$

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

$33\text{in}$ $\displaystyle 33\text{in}$

$31\text{in}$ $\displaystyle 31\text{in}$

$22\text{in}$ $\displaystyle 22\text{in}$

Correct answer:

$33\text{in}$ $\displaystyle 33\text{in}$

Explanation:

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

$\displaystyle P = a+b+c$

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

Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.

So, we can substitute. We get

$P = 11\text{in} + 11\text{in} + 11\text{in}$ $\displaystyle P = 11\text{in} + 11\text{in} + 11\text{in}$

$P = 33\text{in}$ $\displaystyle P = 33\text{in}$

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Example Question #11 : How To Find Perimeter Of A Triangle

Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?

Possible Answers:

$\displaystyle 39$

$\displaystyle 36$

$\displaystyle 38$

$\displaystyle 30$

$\displaystyle 50$

Correct answer:

$\displaystyle 38$

Explanation:

An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.

This makes the perimeter either

$\displaystyle 12+12+13=37$

$\displaystyle 12+13+13=38$

Of our choices, we choose 38.

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SSAT Middle Level Math : Triangles

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Geometry

Example Question #1 : Triangles

Example Question #2 : Geometry

Example Question #1 : Geometry

Example Question #261 : Ssat Middle Level Quantitative (Math)

Example Question #11 : How To Find Perimeter Of A Triangle

All SSAT Middle Level Math Resources

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