Question

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 side 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. Supposed that an isosceles right triangle has legs each length of 3. What is the length of the hypotenuse? Is the Scarecrow’s assertion valid? This question illustrated the true value of a diploma without studying.

Answer 1

The equation that the scarecrow uttered can be expressed mathematically as:

sqrt (C) = sqrt (A) + sqrt (B)

where A, B, and C are the sides of the triangle

 

Since the triangle is an isosceles, therefore A = B and

sqrt (C) = 2 sqrt (A)

given that the measure of the leg is 3, A = 3, C is:

sqrt C = 2 sqrt (3)

sqrt C = 3.464

C = 12

 

In a any triangle, the sum of two sides must be greater than the third side, since in this case C > A + B therefore the Scarecrow is not correct because the correct relationship should be A + B > C.

 

To find the correct hypotenuse, we start with the Pythagorean equation:

C^2 = A^2 + B^2

 

So what the scarecrow mistakenly did was to ignore the “+” symbol during the square root. Taking the square root on both sides, the correct equation is:

C = sqrt (A^2 + B^2)

 

Calculate for C, since A = B = 3:

C = sqrt (3^2 + 3^2)

C = 4.24

 

So now A + B > C and this is now correct.