### All GRE Math Resources

## Example Questions

### 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.

**Possible Answers:**

**Correct answer:**

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 #141 : Plane Geometry

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

**Possible Answers:**

**Correct answer:**

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 #141 : Plane Geometry

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:**

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 #142 : Plane Geometry

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:**

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 #143 : Plane Geometry

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

**Possible Answers:**

**Correct answer:**

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 #22 : Quadrilaterals

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:**

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 #23 : 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:**

**Correct answer:**

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 #145 : Plane Geometry

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

**Possible Answers:**

**Correct answer:**

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 #146 : Plane Geometry

Using the parallelogram shown above, find the length of side

**Possible Answers:**

**Correct answer:**

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 #147 : Plane Geometry

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:**

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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