The owners want to hire a contractor to build a porch along side the parlor. the parlor is rectangular with width of 32 feet and length of 50 feet. the porch will have the same width that on each side of the house. see design plans.

Hello there!

a) Basically, you are adding the length of porch to the original length of the parlor.
Let's say that the newly added porch is x.

(50 + x)(32 + x)
1600 + 50x + 32x + x²
x² + 82x + 1600

b) Just make the polynomial x² + 82x + 1600 equal to 2320.
x² + 82x + 1600 = 2320

subtract 2320 on both sides to make the polynomial equal to 0.
x² + 82x - 720 = 0

factor this
(x - 8)(x + 90) = 0
(x - 8) =0       (x + 90) = 0
       x = 8                 x = - 90
                            (-90ft doesn't make sense. So don't mind about this.)

So the porch should be 8ft.

Hope this helped!