



 
Hi Lyndsay, Suppose the other side has length $y$ cm then the perimeter is $x + x + y + y = 2x + 2y$ cm. But you know this is 50 cm so $2x + 2y = 50 \mbox{ or } x + y = 25.$ Thus $y = 25  x.$ The area, $A$ of a rectangle is the length times the width and hence $A = x \times y$ or \[A = x(25  x).\] There are a couple of ways to approach part (b). If you know some calculus you can treat part (b) as a maxmin problem. Otherwise you can use the fact that the maximum or minimum of the quadratic function $a x^2 + b x + c$ is at the vertex. Penny  


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