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Determine a function a(w) that models the area of the top surface of the swimming pool in terms of the width , w

User Odelu
by
7.4k points

1 Answer

1 vote

Answer:


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

Explanation:

Given


P = 80 ---- perimeter

Required

Write the area as a function of width

The perimeter of a rectangle is:


P =2(l + w)

Where


l \to length\\ w \to width

So, we have:


80 = 2*(l+w)

Divide by 2


40 = l + w

Make l the subject


l =40 - w

The area of a rectangle is:


A = l * w

Substitute:
l =40 - w


A = (40 - w) * w

Hence, the function is:


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

User Jason Landbridge
by
7.6k points