Find the legs of a right-angled triangle if one of them is 7 cm smaller than the other and the hypotenuse is 17.

Let the length of one leg be x cm, and the second (x + 7) cm.By the Pythagorean theorem, we find the legs.
x ^ 2 + (x +7) ^ 2 = 17 ^ 2;
x ^ 2 + x ^ 2 + 14x + 49 = 289;
2x ^ 2 + 14x + 49 – 289 = 0;
2x ^ 2 + 14x – 240 = 0;
D = 14 ^ 2 – 2 * 2 * (- 240) = 196 + 960 = 1156 = 34 ^ 2;
x1 = (- 14 – 34) / 2 * 2 = – 48/4 = – 12 – does not suit the condition of the problem;
x2 = (- 14 + 34) / 2 * 2 = 20: 4 = 5.
This means that the length of one leg is 5 cm, and the second is 5 + 7 = 12 cm.
Answer: 5 cm and 12 cm.