Question

a rancher will use a river as one side of a rectangular enclosure. he needs to build the other three sides using 1000 feet of fencing. he wants the side parallel to the river to be twice the length of the other dimension. what will be the area of the enclosure?

Answer 1

125,000 ft^2

Explanation:

Let the rectangular enclosure have L for the length and W for the width, both in feet.

The perimeter of this enclosure would be:

Per. = 2L + 2W

The rancher will use a river as one side of the enclosure. Let's say it is one of the two L sides. So in terms of fencing, the Perimeter that requires fencing is given by:

Per. Fencing = L + 2W

The rancher has 1,000 feet of fencing:

1,000 ft = L + 2W

The rancher wants the side parallel the river, L, by twice the length of the other dimension, W. We can write that as:

L = 2W

Let's substitute that into the previous equation:

1,000 ft = L + 2W

1,000 ft = 2W + 2W

4W = 1,000 ft

W = 250 feet

This means that L will be 2W or 500 feet

The area of the enclosure will therefore be:

Area = W*L

Area = (250 ft)*(500 ft) = 125,000 ft^2

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