GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #53 : Geometry

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

Possible Answers:

$\small \small 60$

$\small 133$

$\small 132$

$\small 120$

$\small 130$

Correct answer:

$\small 132$

Explanation:

To solve this problem apply the formula: $\small p=2a+b$ .

However, first calculate the length of the missing side by:

$\small p=2(a)+12$

$\small a=12\times5=60$

$\small p=2(60)+12$

$\small p=120+12=132$

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Example Question #1 : Triangles

An obtuse Isosceles triangle has two sides with length and one side length . The length of side $\frac{3}{4}$ ft. If the length of half the length of side , what is the perimeter of the triangle?

Possible Answers:

$1\frac{1}{3}$ ft

$1\frac{1}{2}$ ft

$1\frac{2}{3}$ ft

$\frac{12}{4}$ ft

Correct answer:

$1\frac{1}{2}$ ft

Explanation:

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that $b=\frac{3}{4}$ ft and that the sides with length are half the length of side , find the length of by: $\frac{3}{4}=\frac{6}{8}$ and half of $\frac{6}{8}=\frac{3}{8}$ . Thus, both of sides with length must equal $\frac{3}{8}$ ft.

Now, apply the formula: p=2a+b .

$p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}$

Then, simplify the fraction/convert to mixed number fraction:

$\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$

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Example Question #1 : Triangles

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

Possible Answers:

$\small \frac{35}{3}$

$\small 27$

$\small 18$

$\small 21$

$\small \frac{56}{3}$

Correct answer:

$\small 21$

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

Each of the missing sides equal:

$\small a=\frac{7}{3}\times4=\frac{28}{3}$

Then apply the perimeter formula:
$\small p=\frac{28}{3}+\frac{28}{3}+\frac{7}{3}=\frac{63}{3}=21$

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Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

Isos._gre_series_

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ inches. If the length of $\small b=$ $\sqrt[3]{a}$ , what is the perimeter of the triangle?

Possible Answers:

inches

Correct answer:

inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$b=\sqrt[3]{a}=\sqrt[3]{8}=2$

Then plug each side length into the perimeter formula:

p=2(8)+2=16+2=18

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Example Question #62 : Geometry

Isos._gre_series_

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\sqrt{144}$ inches. If the length of $\small b=a\times \frac{1}{2}$ , what is the perimeter of the triangle?

Possible Answers:

$\small 32$ inches

$\small 18$ inches

$\small 2$ feet

$\small 2.7$ feet

$\small 30$ inches

Correct answer:

$\small 30$ inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$\small a=\sqrt{144}=12$

$\small b=12\times \frac{1}{2}=\frac{12}{2}=6$

Then, apply the perimeter formula by plugging in the side values:

$\small p=2(12)+6=24+6=30$

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Example Question #63 : Geometry

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small \small \frac{3}{12}$ ft. If the length of $\small b=\small a\times \frac{1}{3}$ , what is the perimeter of the triangle?

Possible Answers:

$\small \frac{9}{12}$ foot

$\small \frac{3}{4}$ foot

$\small \frac{1}{4}$ foot

$\small 6$ inches

$\small 7$ inches

Correct answer:

$\small 7$ inches

Explanation:

To solve this problem apply the formula: $\small p=2a+b$ .

However, first calculate the length of the missing side by:

$\small \frac{3}{12}+\frac{3}{12}+(\frac{3}{12}\times\frac{1}{3})$ , Note that $\small \frac{3}{36}=\frac{1}{12}$

$\small \small \frac{6}{12}+\frac{3}{36}=\frac{6}{12}+\frac{1}{12}=\frac{7}{12}$ .

Since, it takes $\small 12$ inches to make one foot, the perimeter is equal to $\small 7$ inches.

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Example Question #64 : Geometry

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small 8$ inches. The length of side $\small b=$ $\small a\times \frac{1}{4}$ . Find the perimeter of the triangle.

Possible Answers:

$\small 18$ inches

$\small 19$ inches

$\small 14$ inches

$\small 13$ inches

$\small 12$ inches

Correct answer:

$\small 18$ inches

Explanation:

To find the perimeter of this triangle, apply the formula:

$\small p=2a+b$

$\small p=2(8)+(8\times \frac{1}{4})$

$\small p=16+\frac{8}{4}$

$\small p=16+2=18$

Note: Since this is an acute Isosceles triangle, the length of the base must be smaller than the length of both of the equivalent sides.

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Example Question #11 : Isosceles Triangles

Isos._cont._gre

The obtuse Isosceles triangle shown above has two sides with length and one side length . The length of side $\small a=$ $\small 43$ inches. Side length $\small b=2a$ . Find the perimeter of the triangle.

Possible Answers:

$\small 172$ inches

$\small 86$ inches

$\small 84$ inches

$\small 15\sqrt{2}$ inches

$\small 129$ inches

Correct answer:

$\small 172$ inches

Explanation:

To find the perimeter of this triangle, apply the perimeter formula:

$\small p=2a+b$

Since, $\small a=43$ , and $\small b=2a$ then $\small b$ must have a value of: $\small 2\times43=86$

This triangle has two side lengths of $\small 43$ inches, and one side length of $\small 86$ inches.

Thus, the solution is:

$\small p=2(43)+86=172$

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Example Question #1251 : Gre Quantitative Reasoning

A triangle has two sides with length and one side length . The length of side $\frac{1}{4}$ yard. If the length of the length of side , what is the perimeter of the triangle?

Possible Answers:

$\small \frac{6}{12}$ yard

$\frac{5}{4}$ yard

$\small \frac{1}{4}$ yard

$\small \frac{7}{12}$ yard

$\small \frac{1}{3}$ yard

Correct answer:

$\frac{5}{4}$ yard

Explanation:

The first step to solving this problem is that we must find the length of length $\small a.$ Since, $\small a$ is $\small 2$ 4 the length of side $\small b$ , use the following steps:

$\small \small b=\frac{1}{4}$
$\small a=\frac{1}{4}\times2=\frac{1}{2}$

Now, apply the formula: $\small p=2a+b$

$\small p=\frac{2}{4}+\frac{2}{4}+\frac{1}{4}=\frac{5}{4}$

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Example Question #11 : Triangles

An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?

Possible Answers:

110

Correct answer:

Explanation:

An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #53 : Geometry

Example Question #1 : Triangles

Example Question #1 : Triangles

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

Example Question #62 : Geometry

Example Question #63 : Geometry

Example Question #64 : Geometry

Example Question #11 : Isosceles Triangles

Example Question #1251 : Gre Quantitative Reasoning

Example Question #11 : Triangles

All GRE Math Resources

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