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. (a) show that A = 72 x - 2x^ (b) factorise completely 72x-2x^2 (c) complete the table for A = 72x-2x^2 (d) draw the graph of A= 72x -2x^2 for 0 < x < 35 on the grid opposite

Answer 1

Answer:

Step-by-step explanation:

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)