Why is the area 76m^2?
George built a swimming pool in his backyard. The dimensions of the pool are: Length: 24 - 2xm & Width: 16 - 2xm
The tiled path around the outside of the pool is x meters wide. Using the binomial expansion we need to find:
a.) the area of the swimming pool
b.) the area of the path
This expression is the expanded form for the area of the pool: (24 - 2x)(16 - 2x) = 384 - 80x + 4x2
The area of the path is whatever is left when we subtract the pool from the total:
Area of path : 384 - (384 - 80x + 4x2)m2 = 80x - 4x2m2
George measures the width of the path & discovers its 1m. What's the area of the pool & path now?
Substituting x = 1 into: 384 - 80x + 4x2 gives: 384 - 80 + 4 = 308m2 therefore the area of the path = 76m2.
Why is the area 76m2?