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 the leg AC = X cm, then, by condition, the length of the leg BC = (X + 7) cm.

Then the AO Pythagorean theorem:

AB ^ 2 = AC ^ 2 + BC ^ 2.

17 ^ 2 = X ^ 2 + (X + 7) ^ 2.

289 = X ^ 2 + X ^ 2 + 14 * X + 49.

2 * X ^ 2 + 14 * X – 240 = 0.

X ^ 2 + 7 * X – 120 = 0.

Let’s solve the quadratic equation.

D = b2 – 4 * a * c = 72 – 4 * 1 * (-120) = 49 + 480 = 529.

X1 = (-7 – √529) / 2 * 1 = (-7 – 23) / 2 = -30 / 2 = -15. (Doesn’t fit because it’s less than 0)

X2 = (-7 + √289) / 2 * 1 = (-7 + 23) 2 = 16/2 = 8 cm.

AC = 8 cm.

BC = 8 + 7 = 12 cm.

Answer: The legs of the triangle are 8 cm and 12 cm.