If x, x + 2 and x + 1 are three sides of a right triangle, what is x

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The sides of a right triangle are x, x + 1 and x + 2. Using Pythagoras' Theorem, (x + 2)^2 = (x + 1)^2 + x^2

=> x^2 + 4x + 4 = x^2 + 2x + 1 + x^2

=> x^2 - 2x - 3 = 0

=> x^2 - 3x + x - 3 = 0

=> x(x - 3) + 1(x - 3) = 0

=> (x + 1)(x - 3) = 0

=> x = -1 and x = 3

The length of a side cannot be negative, ignore x = -1.

The length of the sides of the right triangle are 3, 4 and 5

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