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Verified Answer :

johnkellock

Perimeter =2w+2L= 520.
We can solve this by understanding that the area is maximized by a square
Therefore L=w.

p=2w+2w=520=4w

w=130

Area
 
A=wL=130(130)= 16900 square yards

carlosego

The first thing we are going to do for this case is define variables.

We have then:

w: width

l: length

The perimeter is given by:

\(2w + 2l = 520
\)

The area is given by:


\(A = w * l
\)

The area as a function of a variable is:


\(A (w) = w * (260-w)
\)

Rewriting we have:


\(A (w) = -w ^ 2 + 260w
\)

To obtain the maximum area, we derive:

\(A '(w) = -2w + 260
\)

We equal zero and clear the value of w:

\(-2w + 260 = 0

2w = 260
\)

\(w = \frac{260}{2}

w = 130
\)

Then, the length is given by:

\(l = 260 - w

l = 260 - 130

l = 130
\)

Finally, the maximum area obtained is:

\(A = w * l

A = 130 * 130

A = 16900
\)

Answer:

A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.

The maxium area is 16900 square yards

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