The hypotenuse of a right-angled triangle is 13 cm, and its perimeter is 30. Find the rolls of the triangle?

The solution of the problem:

1. Let us denote by variable x the length of one leg.

2. Knowing that the perimeter of the triangle is 30, the length of the other leg will be:

30 -13 – x = 17 – x.

3. Knowing that the square of the hypotenuse is equal to the sum of the squares of the legs, we compose an equation and find the lengths of the legs:

x ^ 2 + (17 -x) ^ 2 = 13 ^ 2;

2x ^ 2 – 34x + 289 = 169;

2x ^ 2 – 34x + 120 = 0;

Find the discriminant: D = 34 ^ 2 – 4 * 2 * 120 = 196.

x1 = (34 + 14) / 2 * 2 = 12.

x2 = (34 – 14) / 2 * 2 = 5.

Answer: The length of one leg is 12 cm, the length of the other leg is 5 cm.