Question

Find the dimensions of the green space if it's length must be 40 ft less then twice its width with a total area of 33,600 ft^2

I found the equation but I don't know how to find the final width and length

Answer 1

length = 240 units

Width = 140 units

Explanation:

Width = w

Length = 2w - 40 ft

Area = 33,600 square feet

length * width = 33600

(2w - 40) *w = 33600

2w² - 40w = 33600

2w² - 40w - 33600 = 0

Divide the equation by 2

w² - 20w - 16800 = 0

Sum = -20

Product = -16800

Factors = -140 , 120

w² -140w + 120w - 140 * 120 = 0

w(w - 140) + 120(w - 140) = 0

(w - 140)(w + 120) = 0

w +120 = 0 is ignored because width won't be in negative.

w - 140 = 0

w = 140 units

length = 2*140 - 40

= 280 - 40

= 240 units