Question

Use the formulas a = x 2 – y 2, b = 2xy, c = x 2 + y 2 to answer this question. One leg of a right triangle has length 11 and all sides are whole numbers. Find the lengths of the other two sides.

The other leg =
and the hypotenuse =

Answer 1

In order to make use of the formulas, you need a method for choosing x and y. Here, we will choose x=(11+1)/2 = 6 and y=(11-1)/2 = 5. Then
a = 6^2 -5^2 = 36 -25 = 11
b = 2(6)(5) = 60
c = 6^2 +5^2 = 36 +25 = 61

The other leg = 60
and the hypotenuse = 61