Question

Find the dimensions and area of the rectangle of maximum area that can be inscribe in a right triangle with a given hypotenuse length L.

Answer 1

I know I need a primary and seconday equation

Answer 2

It's a square with sides of length L/(2sqrt(2)). Area is (1/8)L^2.

Answer 3

I have to use calculus -optimization

Answer 4

The area will be x*y = x*(b-(b/a)x), with a and b subject to a^2 + b^2 = L^2.

To see this, draw the line with x-intercept (a,0) and y-intercept (0,b).

Good luck.