Chapter 4.1, Problem 12MS

The Scarecrow (ExH). In the 1939 movie The Wizard of Oz, when the brainless Scarecrow is given the confidence to think by the Wizard (by merely handing him a diploma, by the way), the first words the Scarecrow utters are, “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” An isosceles right triangle is just a right triangle having both legs the same length. Suppose that an isosceles right triangle has legs each of length 3. What is the length of the hypotenuse? Is the Scarecrow’s assertion valid? This question illustrates the true value of a diploma without studying.