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Anthony is building a rectangular shaped swimming pool with a perimeter of 80 feet. Determine a function A(w) that models the area of the top surface of the swimming pool in terms of width W. A(w)= For w>0

User Sprhawk
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1 Answer

6 votes

Answer:


A(w) = 40w - w^2

Explanation:

Given


P = 80 --- perimeter

Required

Define the area in terms of width

The perimeter of the pool is:


P =2(l + w)

Where:


l\to length


w\to width

So:


80 =2(l + w)

Divide by 2


40 =l + w

Make l the subject


l = 40-w

The area is then calculated as;


A(w) = l * w

Substitute:
l = 40-w


A(w) = (40 - w) * w


A(w) = 40w - w^2

User Eric Nord
by
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