If a right angles triangle has 3 sides (x, x+1, 5) and then longest side is 5, what is x?

x = 3

The Pythagorean theorem tells you the relationship between the sides is ...

... x² + (x+1)² = 5²

... 2x² +2x +1 = 25

... x(x +1) = 12 . . . . . . subtract 1, divide by 2

We know that 12 = 3·4, so we can match values to the factors in the above equation to get ...

... x = 3

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You can solve by factoring, completing the square, graphing, the quadratic formula, or any other means you might devise to find that the solutions to the equation x² +x -12 = 0 are x = -4 and x = 3. In a geometry problem where x is a length, the solution x = -4 is extraneous.

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