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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

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All SSAT Upper Level Math Resources

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

Example Questions

Example Question #121 : Properties Of Triangles

A triangle with a perimeter of has side lengths of $2a-2, 3a-6, \text{ and }a+2$ . Find the length of the shortest side.

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter.

2a-2+3a-6+a+2=12

6a-6=12

6a=18

a=3 .

Now, subsitute the value of to find the lengths of the sides, then choose the longest side.

2a-2=2(3)-2=4

3a-6=3(3)-6=3

a+2=3+2=5

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Example Question #7 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

The perimeter for the triangle is , and two sides are given. Find the length of the third side.

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter.

Let be the length of the third side.

5+4+x=15

9+x=15

x=6

The length of the third side is .

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Example Question #8 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

The perimeter of the triangle is , and two of the sides are given. What is the length of the third side?

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter.

Let be the length of the third side.

15+20+x=52

35+x=52

x=17

The length of the third side is .

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Example Question #31 : Acute / Obtuse Triangles

The perimeter of the triangle is , and two of the sides are given. What is the length of the third side?

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter of the triangle.

Let be the length of the third side.

3+6+x=13

9+x=13

x=4

The length of the third side is .

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Example Question #32 : Acute / Obtuse Triangles

A triangle has side lenghts of , y+1 , and y-2 . The perimeter of this triangle is . Find the length of the shortest side.

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter of the triangle.

y+y+1+y-2=11

3y-1=11

3y=12

y= 4

Now, we plug in the value of into y-2 to find the length of the shortest side.

4-2=2

The length of the shortest side is .

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Example Question #131 : Properties Of Triangles

The lengths of a triangle with a perimeter of 121 are $2x, 4x,\text{ and }5x$ . Find the length of the longest side.

Possible Answers:

Correct answer:

Explanation:

Add up all the sides to find the perimeter.

2x+4x+5x=121

11x=121

x=11 .

Plugging this value into the sides we get:

$2x, 4x, 5x \rightarrow 2(11), 4(11), 5(11)$

The side lengths of the triangle are $22, 44, \text{ and 55}$ .

The length of the longest side is .

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Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB = 24, BC = 30, AC = 36 ; $\bigtriangleup DEF$ has perimeter 400.

Which of the following is equal to $DF \div DE$ ?

Possible Answers:

1.25

1.2

1.5

$0.8\overline{3}$

$0.\overline{6}$

Correct answer:

1.5

Explanation:

The perimeter of $\bigtriangleup DEF$ is actually irrelevant to this problem. Corresponding sides of similar triangles are in proportion, so use this to calculate $DF \div DE$ , or $\frac{DF}{DE}$ :

$\frac{DF}{DE} = \frac{AC}{AB} = \frac{36}{24} = 1.5$

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Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB = 24, BC = 20, AC = 36 ; $\bigtriangleup DEF$ has perimeter 300.

Evaluate DE + EF .

Possible Answers:

225

Insufficient information is given to answer the problem.

200

165

210

Correct answer:

165

Explanation:

The ratio of the perimeters of two similar triangles is equal to the ratio of the lengths of a pair of corresponding sides. Therefore,

$\frac{DE}{AB}= \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$ and $\frac{EF}{BC}= \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$ , or

$\frac{DE}{AB}=\frac{EF}{BC} = \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$

By one of the properties of proportions, it follows that

$\frac{DE+EF}{AB+BC} = \frac{P_{\bigtriangleup DEF}}{P_{\bigtriangleup ABC }}$

The perimeter of $\bigtriangleup ABC$ is

AB+BC+ AC = 24+ 20+ 36 = 80 , so

$\frac{DE+EF}{24+20} = \frac{300}{80}$

$\frac{DE+EF}{44} = \frac{300}{80}$

$\frac{DE+EF}{44} \cdot 44 = \frac{300}{80} \cdot 44$

DE+EF=165

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Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ ; AB= 12 ; DE = 40 ; $\bigtriangleup DEF$ has perimeter 90.

Give the perimeter of $\bigtriangleup ABC$ .

Possible Answers:

300

360

$53\frac{1}{3}$

Correct answer:

Explanation:

The ratio of the perimeters of two similar triangles is the same as the ratio of the lengths of a pair of corresponding sides. Therefore,

$\frac{P_{\bigtriangleup ABC }}{P_{\bigtriangleup DEF}} = \frac{AB}{DE}$

$\frac{P_{\bigtriangleup ABC }}{90} = \frac{12}{40}$

$\frac{P_{\bigtriangleup ABC }}{90}\cdot 90 = \frac{12}{40} \cdot 90$

$P_{\bigtriangleup ABC} = 27$

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Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$m\angle A + m\angle D = 94^{\circ }$

$m\angle B + m\angle F = 94^{\circ }$

Evaluate $m \angle C + m \angle E$ .

Possible Answers:

$86^{\circ }$

$94^{\circ }$

$172^{\circ }$

$188^{\circ }$

These triangles cannot exist.

Correct answer:

$172^{\circ }$

Explanation:

The similarity of the triangles is actually extraneous information here. The sum of the measures of a triangle is $180 ^{\circ }$ , so:

$m \angle A + m \angle B + m \angle C = 180^{\circ }$

$m \angle D + m \angle E + m \angle F = 180^{\circ }$

$m \angle A + m \angle B + m \angle C +m \angle D + m \angle E + m \angle F = 180^{\circ }+ 180^{\circ }$

$m \angle C + m \angle E + (m \angle A +m \angle D) + (m \angle B + m \angle F )= 360^{\circ }$

$m \angle C + m \angle E +94 ^{\circ } +94 ^{\circ }= 360^{\circ }$

$m \angle C + m \angle E +188 ^{\circ }= 360^{\circ }$

$m \angle C + m \angle E +188 ^{\circ }- 188^{\circ } = 360^{\circ } - 188^{\circ }$

$m \angle C + m \angle E = 172^{\circ }$

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #121 : Properties Of Triangles

Example Question #7 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #8 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #31 : Acute / Obtuse Triangles

Example Question #32 : Acute / Obtuse Triangles

Example Question #131 : Properties Of Triangles

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar

Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar

All SSAT Upper Level Math Resources

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