Let the area be y.















Set y' equal to 0 to find relative extrema:







Square both sides:







Multiply both sides by the denominator on the right



Take positive square roots of both sides:










Take positive square roots of both sides:





Rationalize the denominator:



So the base is 

We find the height but substituting in

height = 

height = 


height = 

height = 

height = 

height = 

height = 

So the dimensions of the right triangle with maximum area has

base and height both equal to  

which is an isosceles right triangle.

Its area is found by substituting  into:



















The maximum area is  or  square inches.

The triangle with maximum area looks like this:



Edwin