Question

The area of a rectangular wall of a barn is 20 square feet. Its length is 6 feet longer than twice the width. Find the length and width of the wall of the barn

Answer 1

....width =x

length = 2x+6

area:

x(2x+6)= 2x²+6x

area = 20 feet²

2x²+6x=20

2x²+6x-20=0

we simplify by 2

x²+3x-10 =0

b²-4ac= 3²-4(1*-10)= 49

Δ =49; √Δ=7

Δ is strictly positive, the equation x²+3x−10=0 admits two solutions.

(b-√Δ)/2a =(-3-7)/2 = -5

(-b+√Δ)/2a =(-3+7)/2 = 2

x1=-5, x2=2

one length is never negative, x= 2

rectangle width = 2 feet

rectangle length = 10 feet

Explanation: