Question

A rectangle has a length of 23 yards less than 4 times its width. If the area of the rectangle is 3131 square yards, find the length of the rectangle.

Answer 1

Length = 101 yards ; width = 31

Explanation:

Length = 4w - 23

width = w

A = lw

3131 = (4w - 23)(w)

3131 = 4w² - 23w

0 = 4w² - 23w - 3131

0 = (4w² + 101)(w - 31)

0 = 4w + 101 ; 0 = w - 31

-101 = 4w 31 = w

-101/4 = w 31 = w

reject - answer, so width = 31 and length = 4w - 23

length = 4(31) - 23

length = 124 - 23

Length = 101