The hypotenuse of a right-angled triangle is 25 cm, and one of the legs is 17 cm larger than the other

The hypotenuse of a right-angled triangle is 25 cm, and one of the legs is 17 cm larger than the other, find the legs of the triangular.

Let’s denote the first leg through x.
We introduce the designation of the second leg: (x + 17) cm.
Let’s compose and solve the equation using the Pythagorean theorem:
(x + 17) ^ 2 + x ^ 2 = 25 ^ 2,

x ^ 2 + 2 * 17 * x + 17 ^ 2 + x ^ 2 = 25 ^ 2,

2x ^ 2 + 34x + 289 = 625,

2x ^ 2 + 34x + 289 – 625 = 0,

2x ^ 2 + 34x – 336 = 0, |: 2

x ^ 2 + 17x – 168 = 0,

a = 1, b = 17, c = 168

D = 172 – 4 * 1 * (-168) = 289 + 672 = 961.

x1 = (-17 – √961) / (2 * 1) = (-17 – 31) / 2 = -48/2 = -24,

x2 = (-17 + √961) / (2 * 1) = (-17 + 31) / 2 = 14/2 = 7.

-24 – does not meet the condition of the problem.

The first leg of a right-angled triangle is 7 centimeters long.
What is the second leg?
7 + 17 = 24 centimeters.

Answer: the legs of a right-angled triangle are 24 cm and 7 cm.