#1**+2 **

1. Let the width = W

The length is 6 more than this = W + 6

So

Area = W * L and the equation becomes

40 = W ( W + 6)

2. We could actually "cheat" at this point and guess the solutions rather easily...but let's do that "boring" math !!!

We have

W(W + 6 ) = 40 simplify

W^2 + 6W = 40

W^2 + 6W - 40 = 0 we need two numbers that sum to 6 and multiply to -40....10 and -4 seem to work...so we have

(W + 10 ) (W - 4) = 0

Set each factor to 0 and solve for W

W + 10 =0 W - 4 = 0

W = -10 (reject...Width has to be positive ) W = 4 this is correct

And the Length is 6 more than this = 4 + 6 = 10 ft

CPhill Apr 26, 2018