A 1.

asked • 10/11/17

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 - 2x
 
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 = 308mtherefore the area of the path = 76m2.
 
Why is the area 76m2?

1 Expert Answer

By:

Michael J. answered • 10/11/17

Tutor
5 (5)

Effective High School STEM Tutor & CUNY Math Peer Leader

Michael J.

In addition to the visualization answer I have given you, did you plug in x=1 into the formula for area of walkway that you came up with?
 
Area of walkway = 80x - 4x2 m2
 
                         = 80 - 4     m2
                         = 76 m2
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10/11/17

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