Answer:
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.
