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## A farmer makes a rectangular enclosure for his animals. He uses a wall for one side and a total of 72 metres of fencing for the other

Question

A farmer makes a rectangular enclosure for his animals.

He uses a wall for one side and a total of 72 metres of fencing for the other three sides.

The enclosure has width x metres and area A square metres.

Show that A = 72x – 21.

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Mathematics
3 years
2021-08-15T19:59:33+00:00
2021-08-15T19:59:33+00:00 1 Answers
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## Answers ( )

Answer:Remember that, for a rectangle of length L and width W, the area is:

A =L*W

And the perimeter is:

P = 2*(L + W)

In this case, we know that:

W = x

Let’s assume that one of the “length” sides is on the part where the farmer uses the wall.

Then the farmer has 72 m of fencing for the other “length” side and for the 2 wide sides, then:

72m = L + 2*x

isolating L we get:

L = (2x – 72m)

Then we can write the area of the rectangle as:

A = L*x = (2x – 72m)*x

A = 2*x^2 – 72m*x

(you wrote A = 72x – 21, I assume that it is incorrect, as the area should be a quadratic equation of x)