Question

the area of a rectangular wall of a barn is 40 square feet. its length is 6 feet longer than the width. find the length and width of the wall of the barn.

Answer 1

Area = length x width
 A= l x w      
  length is 6 ft longer than width, length = width + 6ft
Area = (w+6) x w
        40 sq ft=w^2+ 6w
w^2 + 6w - 40 = 0
(w + 10) (w - 4) = 0
w = -10ft and/or 4ft

distance can't be negative, so 4ft is width, length is 10ft

Answer 2

40 = l * w
l = w + 6

substitute (w + 6) in for l

40 = (w+6)*w
40 = w^2 + 6w
0 = w^2 + 6w - 40
0 = (w + 10) * (w - 4)

w + 10 = 0
w = -10

w - 4 = 0
w = 4

it does not make sense for the width to be negative, so 4 is the correct answer
now go back to one of the original equations, l = w + 6

l = w + 6
l = 4 + 6
l = 10