Find the length of the rectangle.

Question

A rectangle has a length of 33 feet less than 8 times its width. If the area of the rectangle is 7623 square feet, find the length of the rectangle.

Answer 1

L = 8*W - 33

Area = L*W = 7623

W= 7623/L

8*(7623/L) - 33 = L

60984/L - 33 = L

60984/L = L+33

60984 = (L+33)*L

60984 = L² + 33L

L² + 33L -60984 = 0

factor and solve for L

L = - 264, 231 ( can't have a negative length, so we use 231)

to check our answer,

L = 231 = 8*W -33 -> solve for W

W = (231+33) / 8 = 33

231* 33 = 7623

Length of the rectangle is 231 ft.