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.

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