Question

If the square root of 61 is the longest side length in the triangle and the shorter sides are x and x+1, find the value of x that makes the triangle above a right triangle. Write your answer in simplest radical form.

Answer 1

x = 5

Explanation:

You want to find x such that ...

x^2 +(x +1)^2 = 61

2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

x^2 +x -30 = 0 . . . . . . . divide by 2

(x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.