Question

Formula for the perimeter of a rectangle with length l and width

w is given above. If a rectangle has perimeter 24, what could be its length
and width w?

A) l=8, w=4

B) l=10, w=7

C) l=12, w=6

D) l=5, w=7

Answer 1

The perimeter of a rectangle with a perimeter of 24 can be represented by the dimensions given in option A, with a length of 8 and a width of 4.

Step-by-step explanation:

The perimeter of a rectangle is defined as the total distance around the edge of the rectangle, which can be calculated using the formula P = 2l + 2w, where l is the length and w is the width. Given that the perimeter of the rectangle is 24, we need to find the values of length and width that satisfy the equation 2l + 2w = 24.

For option A, if l=8 and w=4, the perimeter is 2(8) + 2(4) = 16 + 8 = 24, which is correct.

For option B, if l=10 and w=7, the perimeter is 2(10) + 2(7) = 20 + 14 = 34, which is incorrect.

For option C, if l=12 and w=6, the perimeter is 2(12) + 2(6) = 24 + 12 = 36, which is incorrect.

For option D, if l=5 and w=7, the perimeter is 2(5) + 2(7) = 10 + 14 = 24, which is correct.

While options A and D both give a perimeter of 24, option D is not possible since the perimeter would actually equal 24. Therefore, the dimensions that could represent a rectangle with a perimeter of 24 are given by option A: length = 8 and width = 4.