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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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Example Questions

Example Question #23 : Triangles

Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

Possible Answers:

$32\: in$

$24\: in$

$72\: in$

None of these answers are correct.

$20\: in$

Correct answer:

$24\: in$

Explanation:

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: 8+12+4=24 .

Because the lengths are in inches, the answer must be in inches as well.

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Example Question #3 : How To Find Perimeter Of A Triangle

If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?

Possible Answers:

Correct answer:

Explanation:

An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.

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Example Question #25 : Triangles

The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?

Possible Answers:

Correct answer:

Explanation:

If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.

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Example Question #25 : Triangles

What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?

Possible Answers:

$21\ \text{ft}$

$12\ \text{ft}$

$9\ \text{ft}$

$14\ \text{ft}$

$36\ \text{ft}$

Correct answer:

$9\ \text{ft}$

Explanation:

Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.

$36\ \text{in}\div 12\ \text{in per ft}=3\ \text{ft}$

In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.

Add the sides together to find the total perimeter.

P=s+s+s=3s

s=3

P=3+3+3=9

The perimeter of the triangle is 9 feet.

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Example Question #26 : Triangles

The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?

Possible Answers:

(11, 6, 2)

(5, 6, 8)

(6, 6, 7)

(2, 8, 9)

(5, 4, 10)

Correct answer:

(6, 6, 7)

Explanation:

Since the triangle is an isoscles, two of the sides must be equal. They must also add to . Looking at the possibilities, only (6, 6, 7) have two sides that are the same length. Now we need to check the triangle inequality to make sure the lengths create a triangle. The triangle inequality is:

A+B>C

A+C>B

B+C>A

Plugging (6, 6, 7) into these inequalities we get:

6+6>7

6+7>6

Therefore, the inequalities hold true thus, (6, 6, 7) creates a triangle. Now we need to look at the sum of the lengths:

6+6+7=19

Therefore, (6, 6, 7) is the correct answer.

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

A triangle has sides feet, feet, and feet. Calculate its perimeter.

Possible Answers:

$360 \;ft$

$50 \;ft$

$25 \;ft$

$100 \;ft$

$240 \;ft$

Correct answer:

$50 \;ft$

Explanation:

The perimeter of any figure is the sum of the lengths of the sides: $12 + 18 + 20 = 50 \;ft$ .

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Example Question #2 : How To Find The Perimeter Of A Triangle

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

Possible Answers:

125

185

150

325

300

Correct answer:

150

Explanation:

By the Pythagorean Theorem, if and are the legs of a right triangle and is its hypotenuse, then

$a^{2} + b^{2} = c^{2}$ .

Set b = 60, c= 65 and solve for :

$a^{2} + 60^{2} = 65^{2}$

$a^{2} + 3,600 = 4,225$

$a^{2} + 3,600 -3,600 = 4,225 -3,600$

$a^{2} = 625$

$\sqrt{a^{2}} =\sqrt{ 625}$

a = 25

The perimeter of the triangle - the sum of the sidelengths - is

P = 25 + 60 + 65 = 150 .

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Example Question #1 : Plane Geometry

What is the perimeter of an equilateral triangle with a side length ?

Possible Answers:

Correct answer:

Explanation:

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

P=4+4+4=12

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Example Question #1 : Triangles

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

Possible Answers:

30cm

16cm

19cm

24cm

28cm

Correct answer:

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 . Therefore, the answer is 28cm .

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Example Question #2 : Plane Geometry

A right triangle has legs feet and feet long. What is its perimeter, in inches?

Possible Answers:

$504 \textrm{ in}$

$432 \textrm{ in}$

$216 \textrm{ in}$

$864 \textrm{ in}$

$252 \textrm{ in}$

Correct answer:

$432 \textrm{ in}$

Explanation:

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

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

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

$36 \times 12 = 432$ inches

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #23 : Triangles

Example Question #3 : How To Find Perimeter Of A Triangle

Example Question #25 : Triangles

Example Question #25 : Triangles

Example Question #26 : Triangles

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

Example Question #2 : How To Find The Perimeter Of A Triangle

Example Question #1 : Plane Geometry

Example Question #1 : Triangles

Example Question #2 : Plane Geometry

All SSAT Middle Level Math Resources

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