12. A flat, square roof needs a square patch in the corner to seal a leak. The side length of

the roof is (x + 12) ft and the side length of the patch is x ft. What is the area of the

good part of the roof?

Step-by-step explanation:

Area of the good part = area of whole roof - area of bad part

Since the roof is a square roof, the area will be calculated using the formulae for area of a square

Area of a square = length²

Area of good part = (x+12) ²-x²

A = { (x+12) (x+12) } - x²

A = (x²+12x+12x+144) - x²

Open the bracket and rearrange the equation

A = x²-x²+24x+144

A = (24x+144) ft