Question

The area of a rectangular wall of a barn is 300 square feet. its length is 10 feet longer than twice its width. find the length and width of the wall of the barn.

Answer 1

L * W = 300 sq ft
Length is 10 ft greater than twice the width.
L = 2W + 10
Substituting
(2W+10)*W = 300
2W^2 + 10W = 300
Divide both sides by 2
W^2 + 5W = 150
W^2 + 5W - 150 = 0
Factor
(W +15)(W -10) = 0

Roots are W=-15 and W=10.
A negative width is impossible, so W=10
L = 2W + 10
L = 2(10) + 10
L = 30

length = 30 feet, width = 10 feet

Check: 30*10 = 300