The sum of the legs of a right triangle is 36 cm. For what lengths of the sides will the square of the hypotenuse be a minimum?
We can do this in two ways: by lateral thinking or in the robust mathematical way,
Let's do the first way , assuming both legs are 18 cm. Then the square of the hypotenuse will be
If we change this to
The mathematical way:
If one leg is
The square of the hypotenuse is then:
Now we have to find the minimum of: