The length, in cm, of the sides of a right angled triangle are x, (x+2)...

Explanation

The longest side of a right angle triangle is the hypotenuse.

\((x + 2)^{2} = x^{2} + (x + 1)^{2}\)

\(x^2 + 4x + 4 = x^2 + x^2 + 2x + 1\)

\(2x^{2} - x^{2} + 2x - 4x + 1 - 4 = 0\)

\(x^{2} - 2x - 3 = 0\)

\(x^{2} - 3x + x - 3 = 0 \implies x(x - 3) + 1(x - 3) = 0\)

\((x - 3)(x + 1) = 0 \implies \text{x = 3 or -1}\)

\(x > 0 \implies x = 3\)

The longest side = 3 + 2 = 5.