# How do you find the right triangle of maximum area if the sum of the lengths of the legs is 5?

##### 1 Answer

Jun 7, 2015

Call x and y the 2 legs.

Area of the right triangle:

Given: x + y = 5 --> y = 5 - x

Then,

s maximum when the derivative s' = 0 -> 2x - 5 = 0 -->

The area is max when both legs are equals.

Check:

When x = 2, y = 3, the area is

When x = 1, and y = 4, the area is