In a right-angled triangle, one of the legs is 39 cm, and the hypotenuse is 13 cm

In a right-angled triangle, one of the legs is 39 cm, and the hypotenuse is 13 cm longer than the other leg. Calculate the hypotenuse and the other leg of the triangle.

x cm – another leg.

x + 13 cm – hypotenuse.

Using the Pythagorean theorem, we define the second leg.

x ^ 2 = (x + 13) ^ 2 – 39 ^ 2;

x ^ 2 = x ^ 2 + 26x + 169 – 1521;

26x = 1521 – 169;

26x = 1352;

x = 1352: 26;

x = 52.

The other leg is 52 cm.

Let’s define the hypotenuse of the triangle.

x + 13 = 52 + 13 = 65 cm.

Answer: the hypotenuse of the triangle is 65 cm, and the other leg is 52 cm.