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

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

Let one leg be x cm, the second x + 17 cm.
Taking into account the condition of the problem, we compose an equation.
x ^ 2 + (x + 17) ^ 2 = 625;
x ^ 2 + x ^ 2 + 34x + 289 = 625;
2x ^ 2 + 34x-336 = 0;
x ^ 2 + 34x-168 = 0;
By Vieta’s theorem:
x1 = -24 – length cannot be negative.
x2 = 7;
One leg x = 7 cm.
The second leg is x + 17 = 7 + 17 = 24 cm.
Answer: 7 cm; 24 cm.