3405.12 – Impossible Rectangle?

Can a rectangle with a $48 \ \cm$ perimeter to have an area of $150 \ \cm^2$ ? Explain why or why not.

Solution

It is impossible.

The maximum possible area for a given perimeter occurs when the rectangle is a square. If the perimeter is $48 \ \cm$ , each side of the square is $12 \ \cm$ , and the area would be only $144 \ \cm^2$ .

So it is not possible for the rectangle to have an area of $150 \ \cm^2$ .