# 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?

##### 1 Answer

Jan 8, 2016

We can do this in two ways: by lateral thinking or in the robust mathematical way,

#### Explanation:

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

Even

And

**The mathematical way:**

If one leg is

The square of the hypotenuse is then:

Now we have to find the minimum of: