## Example Questions

### 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 #7 : 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:

### Example Question #141 : Geometry

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 #151 : Geometry

A parallelogram has a base of . The perimeter of the parallelogram is . Find the length 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 . To solve for the missing side, work backwards using the perimeter formula:

, where  and  are the measurements of adjacent sides.

Thus, the solution is:

### Example Question #152 : Geometry

A quadrilateral has equal sides, each with a length of .

Quantity A: The area of the quadrilateral.

Quantity B: The perimeter of the quadrilateral.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The relationship cannot be determined.

Explanation:

We are told that the shape is a quadrilateral and that the sides are equal; beyond that, we do not know what specific kind of kind of quadrilateral it is, outside of the fact that it is a rhombus. The perimeter, the sum of the sides, is .

If this shape were a square, the area would also be ; however, if the interior angles were not all equivalent, the area would be smaller than this.

The relationship cannot be determined.

### Example Question #1 : Rectangles

A rectangle has an area of 48 and a perimeter of 28.  What are its dimensions?

2 x 24

0.25 x 192

1 x 48

6 x 8

16 x 3

6 x 8

Explanation:

We can set up our data into the following two equations:

(Area) LH = 48

(Perimeter) 2L + 2H = 28

Solve the area equation for one of the two variables (here, length): L = 48 / H

Place that value for L into ever place you find L in the perimeter equation: 2(48 / H) + 2H = 28; then simplify:

96/H + 2H = 28

Multiply through by H: 96 + 2H2 = 28H

Get everything on the same side of the equals sign: 2H2 - 28H + 96 = 0

Divide out the common 2: H2 - 14H + 48 = 0

Factor: (H - 6) (H - 8) = 0

Either of these multiples can be 0, therefore, consider each one separately:

H - 6 = 0; H = 6

H - 8 = 0; H = 8

Because this is a rectangle, these two dimensions are the height and width.  If you choose 6 for the "height" the other perpendicular dimension would be 8 and vice-versa.  Therefore, the dimensions are 6 x 8.

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