GRE Math : Plane Geometry

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Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Parallelogram gre

Using the parallelogram shown above, find the sum of the two sides adjacent to the base.

Possible Answers:

$2\sqrt{29}$

$\sqrt{58}$

$2+\sqrt{29}$

$\sqrt{58}-2$

$\sqrt{29}$

Correct answer:

$2\sqrt{29}$

Explanation:

To find one of the adjacent sides to the base, first note that the interior triangles represented by the red vertical lines must have a height of and a base length of 10-8=2. Then, apply the formula: a^2+b^2=c^2 to find the length of one side.

Thus, the solution is:

2^2+5^2=c^2

4+25=c^2

29=c^2

$c=\sqrt{29}$

Therefore, the sum of the two sides is:

$\sqrt{29}+\sqrt{29}=2\sqrt{29}$

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Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of . The perimeter of the parallelogram is 278 . Find the sum of the two adjacent sides to the base.

Possible Answers:

148

$\textup{Not enough information is provided.}$

130

204

Correct answer:

130

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of and two base sides each with a length of . In this question, you are provided with the information that the parallelogram has a base of and a total perimeter of 278 . Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

278=2(74+b)

278=148+2b

2b=278-148=130

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Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of . The perimeter of the parallelogram is . Find the length of an adjacent side to the base.

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of and two base sides each with a length of Since the perimeter and one base length is provided in the question, work backwards using the perimeter formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

30=2(7+b)

30=14+2b

2b=30-14=16

$b=\frac{16}{2}=8$

Check:

30=7+7+8+8

30=14+16

30=30

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Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base measurement of $24\textup{mm}$ . The perimeter of the parallelogram is $80\textup{mm}$ . Find the measurement of an adjacent side to the base.

Possible Answers:

$160\textup{mm}$

$12\textup{mm}$

$36\textup{mm}$

$16\textup{mm}$

$8\textup{mm}$

Correct answer:

$16\textup{mm}$

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of $16\textup{mm}$ and two base sides each with a length of $24\textup{mm}$ . In this question, you are provided with the information that the parallelogram has a base of $24\textup{mm}$ and a total perimeter of $80\textup{mm}$ . Thus, work backwards using the perimeter formula in order to find the length of one missing side that is adjacent to the base.

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

80=2(24+b)

80=48+2b

2b=80-48=32

$b=\frac{32}{2}=16$

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Example Question #5 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of . The perimeter of the parallelogram is . Find the sum of the two adjacent sides to the base.

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of and two base sides each with a length of . In this question, you are given the information that the parallelogram has a base of and a total perimeter of . Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

82=2(16+b)

82=32+2b

2b=82-32=50

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Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of $55\textup{mm}$ . An adjacent side to the base has a length of $45\textup{mm}$ . Find the perimeter of the parallelogram.

Possible Answers:

$150\textup{mm}$

$175\textup{mm}$

$200\textup{mm}$

$250\textup{mm}$

$100\textup{mm}$

Correct answer:

$200\textup{mm}$

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of $45\textup{mm}$ and two base sides each with a length of $55\textup{mm}$ . To find the perimeter of the parallelogram apply the formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

p=2(55+45)

p=2(100)

p=200

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Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base measurement of $140\textup{ inches}$ . The perimeter of the parallelogram is $46\textup{ feet}$ . Find the measurement for an adjacent side to the base.

Possible Answers:

$36\textup{ inches}$

$136\textup{ inches}$

$272\textup{ inches}$

$23\textup{ feet}$

$\textup{Not enough information is provided}$

Correct answer:

$136\textup{ inches}$

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of $136\textup{ inches}$ and two base sides each with a length of $140\textup{ inches}$ . However, to solve this problem you must first convert the provided perimeter measurement from feet to inches. Since an inch is $\frac{1}{12}$ of foot, feet is equal to $46\times12=552$ inches.

Now, you can work backwards using the formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

552=2(140+b)

552=280+2b

2b=552-280=272

$b=\frac{272}{2}=136$

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Example Question #6 : How To Find The Length Of The Side Of A Parallelogram

Parallelogram gre

Using the parallelogram shown above, find the length of side

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of and two base sides each with a length of 18. Since the perimeter and one base length is provided in the question, work backwards using the perimeter formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

68=2(18+b)

68=36+2b

2b=68-36=32

$b=\frac{32}{2}=16$

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Example Question #4 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of . The perimeter of the parallelogram is . Find the sum of the two adjacent sides to the base.

Possible Answers:

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of and two base sides each with a length of . In this question, you are provided with the information that the parallelogram has a base of and a total perimeter of . Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

72=2(22+b)

72=44+2b

2b=72-44=28

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Example Question #21 : Quadrilaterals

A parallelogram has a base of . An adjacent side to the base has a length of . Find the perimeter of the parallelogram.

Possible Answers:

47.5

Correct answer:

Explanation:

A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of and two base sides each with a length of 28. To find the perimeter of the parallelogram apply the formula:

$\textup{Perimeter}=2(a+b)$ , where and are the measurements of adjacent sides.

Thus, the solution is:

p=2(28+18)

p=2(46)

p=92

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GRE Math : Plane Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Example Question #5 : How To Find The Length Of The Side Of A Parallelogram

Example Question #2 : How To Find The Length Of The Side Of A Parallelogram

Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

Example Question #6 : How To Find The Length Of The Side Of A Parallelogram

Example Question #4 : How To Find The Length Of The Side Of A Parallelogram

Example Question #21 : Quadrilaterals

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