Question

Alex has 520 yards of fencing to enclose a rectangular area.

A retangle that maximises the enclosed area has a length of _ yards and a width of _ yards.

The maxium area is _____ yards

Answer 1

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

Answer 2

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:

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The area is given by:

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The area as a function of a variable is:

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Rewriting we have:

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To obtain the maximum area, we derive:

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We equal zero and clear the value of w:

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Then, the length is given by:

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Finally, the maximum area obtained is:

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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