The sum of the legs of a right-angled triangle is 23 cm. Find the coquettes of a triangle if its hypotenuse is 17 cm.

x is the first leg;

(23 – x) – second leg;

by the Pythagorean theorem; x ^ 2 + (23 – x) ^ 2 = 17 ^ 2;

x ^ 2 + 529 – 46x + x ^ 2 = 289;

2x ^ 2 – 46x + 529 – 289 = 0;

2x ^ 2 – 46x + 240 = 0;

x ^ 2 – 23x + 120 = 0;

D = (-23) ^ 2 – 4 * 1 * 120 = 529 – 480 = 49; √D = 7;

x1 = (23 + 7) / 2 = 30/2 = 15 (cm) – the first 1st leg;

x2 = (23 – 7) / 2 = 16/2 = 8 (cm) – the second 1st leg;

23 – x1 = 23 – 15 = 8 (cm) – the first 2nd leg;

23 – x2 = 23 – 8 = 15 (cm) – second 2nd leg.

The legs can be 15 cm and 8 cm, or 8 cm or 15 cm, which is the same.

Answer. 15 cm, 8 cm.