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In Mathematics / College | 2025-07-07

If the perimeter of the parallelogram is 100, find the lengths of the sides.
A. 22 and 28
B. 18 and 15
C. 14 and 12
D. 24 and 22

Asked by nombom

Answer (2)

The problem involves finding the side lengths of a parallelogram given its perimeter.

The perimeter of a parallelogram is P = 2 ( a + b ) , where a and b are the lengths of the sides.
Given P = 100 , we have a + b = 50 .
We check each option to see which pair of side lengths sums to 50.
The correct option is a. 22 and 28, since 22 + 28 = 50 . Therefore, the lengths of the sides are 22 and 28 ​ .

Explanation

Problem Analysis We are given a parallelogram with a perimeter of 100. Our goal is to find the lengths of its sides from the given options.

Perimeter Formula The perimeter of a parallelogram is given by the formula P = 2 ( a + b ) , where a and b are the lengths of the adjacent sides. We are given that the perimeter P = 100 . Therefore, we have the equation 2 ( a + b ) = 100 . Dividing both sides by 2, we get a + b = 50 .

Checking the Options Now, we will check each option to see which pair of side lengths satisfies the condition a + b = 50 .


a. 22 and 28: 22 + 28 = 50 . This option satisfies the condition. b. 18 and 15: 18 + 15 = 33 . This option does not satisfy the condition. c. 14 and 12: 14 + 12 = 26 . This option does not satisfy the condition. d. 24 and 22: 24 + 22 = 46 . This option does not satisfy the condition.

Final Answer Only option a. 22 and 28 satisfies the condition a + b = 50 . Therefore, the lengths of the sides of the parallelogram are 22 and 28.

Examples
Imagine you're designing a rectangular garden with a fence around it. If you know you have 100 feet of fencing material and want to determine the possible lengths of the sides, you can use the perimeter formula for a parallelogram (which is the same as for a rectangle). If one side is 22 feet, the adjacent side must be 28 feet to use all 100 feet of fencing. This ensures your garden fits perfectly within the fenced area.

Answered by GinnyAnswer | 2025-07-07

The perimeter of a parallelogram is given by the formula P = 2 ( a + b ) . When solving for side lengths with a perimeter of 100, only the pair 22 and 28 satisfies the equation a + b = 50 . Thus, the correct choice is option A: 22 and 28.
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Answered by Anonymous | 2025-07-25

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