Find the dimensions of a rectangle with a perimeter of 192 feet that has the maximum area

Let be the dimensions of the rectangle. Since the perimeter is 192, we know that

The area of the rectangle is the product of the dimensions. We can use the expression for we just found to write it as

This is a parabola, opening downwards, so the maximum will be its vertex, whose -coordinate we can find using

And we deduce

We just found out a very well known theorem: given a fixed perimeter, the rectangle with the maximum area is actually the square.

it reflected because of the glass maube

step-by-step explanation: