HELP WITH QUADRATIC EQUATIONS

Question

A rectangular lawn has a legnth that is 2m longer than the width. the area of the lawn is 8m^2. What is the quadratic equation?

Answer 1

L= 2+ W

Area = A = LW = (2+W)W = 2W + W^2

A = 8 = W^2 + 2W

W^2 + 2W -8 = 0

(W+4)(W-2) = 0

W =2 or -4

L = 4 or -2

ignore the negative solutions

Length = 4 meters

Width = 2 meters

Area = LW = 4(2) = 8 m^2

Answer 2

Let x = the width the lawn.

Then x + 2 = the length of the lawn.

Since area = width times length and we know the ares is 8m^2 (8 square meters).

x(x+2) = 8

x^2 + 2x = 8

x^2 + 2x - 8 = 0

(x+4)(x-2) = 0

This gives us x = 2 (We reject the impossible answer x = -4)

So the width of the lawn is 2 meters and the length of the lawn is 2 + 2 or 4 meters