Question

A rectangle has a length of 30 feet less than 8 times its width. If the area of the rectangle is 3542 square feet, find the length of the rectangle.

Answer 1

Step-by-step explanation:

length = 8×width - 30

length × width = 3542

(8×width - 30)×width = 3542

8width² - 30width - 3542 = 0

4width² - 15width - 1771 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 4

b = -15

c = -1771

width = (15 ± sqrt((-15)² - 4×4×-1771))/(2×4) =

= (15 ± sqrt(225 + 28336))/8 =

= (15 ± sqrt(28561))/8 = (15 ± 169)/8

width1 = (15 + 169)/8 = 184/8 = 23 ft

width2 = (15 - 169)/8 = -154/8 = -19.25 ft

a negative number for an actual length does not make any sense, so, only width = 23 ft is a valid solution.

length = 8×width - 30 = 8×23 - 30 = 184 - 30 = 154 ft