Find the lengths of the sides of a right-angled triangle if it is known that one of the legs

Find the lengths of the sides of a right-angled triangle if it is known that one of the legs is 1 cm less than the hypotenuse, and the other is 2 cm.

Let’s denote the length of the hypotenuse x centimeters. Then the length of one of the legs of the triangle will be (x – 1), and the length of the second will be (x – 2).
Let’s use the Pythagorean theorem and compose the equation:
(x – 1) ² + (x – 2) ² = x²
x² – 2x + 1 + x² – 4x +4 = x²
x² – 6x + 5 = 0
D = b² – 4ac = 36 – 20 = 16, D> 0, the equation has two roots.
x1 = (6 – √16) / 2 = 1;
x2 = (6 + √16) / 2 = 5.
The first root of the equation does not suit us.
x = 5 (cm) – hypotenuse;
x – 1 = 4 (cm) – one leg;
x – 2 = 3 (cm) – second leg.
Answer: 3, 4, 5 – sides of a right-angled triangle.