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

Let’s solve this problem using the equation.

Let the first leg be x centimeters, then the second leg is (x + 17) centimeters. We know that the hypotenuse of a right-angled triangle is 25 centimeters. By the Pythagorean theorem, we compose the equation:

x ^ 2 + (x + 17) ^ 2 = 25 ^ 2;

x ^ 2 + x ^ 2 + 17 ^ 2 + 2 * 17 * x = 625;

x ^ 2 + x ^ 2 + 289 + 34 * x – 625 = 0;

2 * x ^ 2 + 34 * x – 336 = 0;

D = b ^ 2 – 4 * a * c = 1156 – 4 * 2 * (-336) = 1156 + 2688 = 3844;

x = (-34 + 62) / 2 * 2 = 28/4 = 7 centimeters – the first leg;

7 + 17 = 24 centimeters – second leg;

x = (-34 – 62) / 2 * 2 = -96/4 = -24 – does not satisfy the condition.

Answer: 24 centimeters; 7 centimeters.