The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 4 inches less than 4 times the perimeter. What is the length and width of the rectangle?

Answer 1

L=7+w

A= 4P-4

LW = 4(2L+2W) -4

(7+W)W = 4(14+2W +2W) -4

W^2 +7W = 56 + 16W -4

W^2 -9W -52 =0

(W-13)(W+4) =0

W =13 inches Wide

L = 20 inches Long

Area = LW = 20x13 = 260 in^2

Perimeter = 2L+2W = 40+26 = 66 in.

A = 4P +4 = 4(66) - 4 = 264-4 = 260 in^2

there is a slight problem with the problem comparing

A to P as they have different units, squared units vs. linear units,

but this seems to be what they expect for a solution