Answer:
x = 3
Explanation:
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
_____
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.
