3405.12 – Impossible Rectangle?

Can a rectangle with a $48$ cm perimeter to have an area of $150$ square cm? 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 $144$ square cm.

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