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.

  x = 5

Step-by-step 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.

42

step-by-step explanation: