Find the rule connecting A and x

Question

A farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence. If the width of the yard is x m and the area inside the yard is A m², write down the rule connecting A and x

Answer 1

The Area of the yard is A.  We know that A = L*W. Since W=x, this is:

     A = L*x

 

Now, the total perimeter of a rectangle is P = L + W + L + W = 2L + 2W

     But, W=x, so:

        P = 2L + 2x

 

Assume that the existing fence is along the Length, so:  60 = W + L + W = L + 2x

                L = 60 - 2x

 

A = L*x

A = (60-2x)(x)

A = 60x - 2x²

 

or

A = -2x² + 60x          [A is a function of x]