# GRE Math : How to find the length of the side of a parallelogram

## Example Questions

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

The sum of the two bases in a parallelogram is  An adjacent side to the bases is  the length of one of the two base measurements. Find the length of one side that is adjacent to the bases.

Explanation:

In this problem, you are told that the sum of the two bases in a parallelogram is  Since the two bases must be equivalent, each side must equal: . Additionally, the problem states that the adjacent sides are  the length of the bases. Therefore, an adjacent side to the base must equal:

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

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

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  Then, apply the formula:  to find the length of one side.

Thus, the solution is:

Therefore, the sum of the two sides is:

### 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 sum of the two adjacent sides to the base.

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.

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### 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 length of an adjacent side to the base.

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:

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

Check:

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

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

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 length of one missing side that is adjacent to the base.

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### Example Question #6 : 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.

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.

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

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

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

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 . To find the perimeter of the parallelogram apply the formula:

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### Example Question #8 : How To Find The Length Of The Side Of A Parallelogram

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

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 . However, to solve this problem you must first convert the provided perimeter measurement from feet to inches. Since an inch is  of  foot,  feet is equal to inches.

Now, you can work backwards using the formula:

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### Example Question #9 : How To Find The Length Of The Side Of A Parallelogram

Using the parallelogram shown above, find the length of side

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:

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### Example Question #10 : 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.

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.

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

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