I'm a bit confused

Question

If the area of the rectangle below is 80 square feet, solve for  and then find the dimensions. 

l = x-3

w = x-5

Answer 1

The area of a rectangle is Length x Width

A = L x W

A = 80

L = x-3

W = x-5

A = (x-3)(x-5)

80 = x² - 8x + 15 [FOIL the quadratic]

0 = x² - 8x - 65 [Subtract 80 from each side]

0 = (x-13)(x+5) [factor the quadratic]

Therefore x = 13 or x = -5

We must now check to make sure the length and width make sense based on the x values in the solution

When x=13

L = 13-3 = 10

W = 13-5 = 8

A = (10)(8) = 80 This checks out

When x = -5

L = -5-3 = -8

W = -5-5 = -10

We can't have negative width and length, so x=-5 is not a valid solution.

Therefore the only solution for x is x=13