SSAT Upper Level Math : Acute / Obtuse Triangles

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

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Example Questions

Example Question #1 : Acute / Obtuse Triangles

If the vertex angle of an isosceles triangle is 30 degrees, what is the value of the angle that is exterior to one of the base angles?

Possible Answers:

\(\displaystyle 105^{\circ}\)

\(\displaystyle 75^{\circ}\)

\(\displaystyle 15^{\circ}\)

\(\displaystyle 150^{\circ}\)

\(\displaystyle 30^{\circ}\)

Correct answer:

\(\displaystyle 105^{\circ}\)

Explanation:

First, you subtract one angle so \(\displaystyle 180-30 = 150\). Because there are 2 base angles you divide that value by 2 to get 75 Degrees. The exterior angle and the base angle are supplementary angles so \(\displaystyle 180-75 = 105\).

Example Question #2 : Acute / Obtuse Triangles

The side lengths of a triangle are \(\displaystyle 2x, 8x, \text{ and } 4x\). Find the perimeter of the triangle.

Possible Answers:

\(\displaystyle 12x\)

\(\displaystyle 14\)

\(\displaystyle 30x\)

\(\displaystyle 14x\)

Correct answer:

\(\displaystyle 14x\)

Explanation:

To find the perimeter of a triangle, add up its side lengths.

\(\displaystyle 2x+8x+4x=14x\)

Example Question #3 : Acute / Obtuse Triangles

The side lengths of a triangle, in inches, are \(\displaystyle 5, 6, 10\). Find the perimeter of this triangle.

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 21\)

\(\displaystyle 11\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 21\)

Explanation:

Find the perimeter of a triangle by adding up all its sides.

\(\displaystyle 5+6+10=21\)

Example Question #4 : Acute / Obtuse Triangles

A triangle has side lengths \(\displaystyle 5\)\(\displaystyle 12\), and \(\displaystyle 14\). What is the perimeter of this triangle?

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 36\)

\(\displaystyle 31\)

\(\displaystyle 26\)

Correct answer:

\(\displaystyle 31\)

Explanation:

To find the perimeter of a triangle, add up all the side lengths.

\(\displaystyle \text{Perimeter}=5+12+14=31\)

Example Question #5 : Acute / Obtuse Triangles

In terms of \(\displaystyle x\), find the perimeter of a triangle with side lengths of \(\displaystyle \text{12x, 4x, x-2}\).

Possible Answers:

\(\displaystyle 14x-8\)

\(\displaystyle 17x-2\)

\(\displaystyle 7x-2\)

\(\displaystyle 17x+2\)

Correct answer:

\(\displaystyle 17x-2\)

Explanation:

To find the perimeter of a triangle, add up all of its sides.

\(\displaystyle \text{Perimeter}=12x+4x+x-2=17x-2\)

Example Question #6 : Acute / Obtuse Triangles

In terms of \(\displaystyle a\), find the perimeter of a triangle with side lengths \(\displaystyle \text{5a-2, 3a, 9a-9}\).

Possible Answers:

\(\displaystyle 17a-7\)

\(\displaystyle 7a-7\)

\(\displaystyle 19a+5\)

\(\displaystyle 17a-11\)

Correct answer:

\(\displaystyle 17a-11\)

Explanation:

To find the perimeter of a triangle, add up all of its sides.

\(\displaystyle \text{Perimeter}=5a-2+3a+9a-9=17a-11\)

Example Question #7 : Acute / Obtuse Triangles

In terms of \(\displaystyle b\), find the perimeter of a triangle with side lengths of \(\displaystyle \text{b+6, b-8, 4b-2}\).

Possible Answers:

\(\displaystyle 6b-4\)

\(\displaystyle 2b+4\)

\(\displaystyle 2b-4\)

\(\displaystyle 6b+4\)

Correct answer:

\(\displaystyle 6b-4\)

Explanation:

To find the perimeter of a triangle, add up all of its sides.

\(\displaystyle \text{Perimeter}=b+6+b-8+4b-2=6b-4\)

Example Question #8 : Acute / Obtuse Triangles

In terms of \(\displaystyle c\), find the perimeter of a triangle with side lengths of \(\displaystyle \text{3c-9, -c+10, and 2c-1}\).

Possible Answers:

\(\displaystyle 5c+1\)

\(\displaystyle 5c\)

\(\displaystyle 4c\)

\(\displaystyle 4c-1\)

Correct answer:

\(\displaystyle 4c\)

Explanation:

To find the perimeter of a triangle, add up all of its sides.

\(\displaystyle \text{Perimeter}=3c-9-c+10+2c-1=4c\)

Example Question #9 : Acute / Obtuse Triangles

Find the perimeter of a triangle with side lengths \(\displaystyle 45, 40,\text{ and }35\).

Possible Answers:

\(\displaystyle 130\)

\(\displaystyle 120\)

\(\displaystyle 115\)

\(\displaystyle 110\)

Correct answer:

\(\displaystyle 120\)

Explanation:

To find the perimeter of a triangle, add up all of its sides.

\(\displaystyle \text{Perimeter}=45+35+40=120\)

Example Question #10 : Acute / Obtuse Triangles

Bill has a triangular garden that he needs to fence. The garden has side lengths of \(\displaystyle \text{9 feet, 10 feet, and 12 feet}\). In feet, how much fencing will Bill need?

Possible Answers:

\(\displaystyle 36ft\)

\(\displaystyle 35ft\)

\(\displaystyle 31ft\)

\(\displaystyle 22ft\)

Correct answer:

\(\displaystyle 31ft\)

Explanation:

To find how much fencing Bill needs, you will need to find the perimeter of the triangle. The perimeter of a triangle is found by adding up all the sides together.

\(\displaystyle \text{Perimeter}=9+10+12=31\)

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