The length of a rectangle is seven inches more than the width. The perimeter is 54 inches. Find the length and the width.

length is 30.5 and width is 23.5

Step-by-step explanation:

first do 54 - 7 to see how much each is, then add back the 7 to the one with 7 extra, length. 54 - 7 is 47. 47 split in 2 is 23.5. That is width. Add 7 extra to length. 23.5 + 7 is 30.5. length is 30.5.

The perimeter of a rectangle is equal to the sum of twice the rectangle's length and twice the rectangle's width:

P = 2l + 2w

and, here, P = 54 inches.

We are told that the length is seven inches more than the width. So, l = w + 7. We can substitute w + 7 for l in the equation for the perimeter:

P = 2(w + 7) + 2w = 54.

We can now solve for w:

2w + 14 + 2w = 54

4w = 40

w = 10 inches.

Now that we know the width, we can determine the length.

54 = 2l + 2w

54 = 2l + 2(10)

34 = 2l

l = 17 inches.

Thus, the length is 17 inches, and the width is 10 inches.

To check our work, a length of 17 inches is seven inches more than the width of 10 inches, and the perimeter of a rectangle with a length of 17 inches and a width of 10 inches is 17 + 17 + 10 + 10 = 54 inches.