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
