Paper 2 · June 2013 · Maxima and minima

A farmer has 56 m of mesh wire, which he uses as the complete perimeter of a rectangular pen for his goats. The width of the pen is $x$ m. Write down an expression, in terms of $x$ , for the area $A$ of the pen.

Model answer

28x - x^2

Also accepted: 28x-x^2, x(28-x), x(28 - x), 28x - x², -x^2 + 28x

Explanation

The 56 m of wire is the perimeter, so

2x+2L=56

and the length is

L=28-x

. The area is therefore

A=x(28-x)=28x-x^2

Derived from ZIMSEC Mathematics Paper 2, June 2013, Q1

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