hi draketcg

Welcome to the forum!

If you call the length x then the width must be (24 - 2x)/2 = 12 - x

So the area is x(12-x)

So the question is, can you make that equal to 40 ?

If you try to solve that using the quadratic formula:

There are no real values of x to solve that square root so it would seem it is not possible.

To find the biggest area I'll make a graph first :

You can see from the graph ( at the end ) that the maximum is below 40, so that confirms the statement above.

Quadratics are symmetrical so the maximum will be at x = 6

Or use calculus to find the maximum.

So biggest area = 6(12-6) = 36

Bob