The leg of a right-angled triangle is 9 cm, and the hypotenuse and the second leg are 5: 4?

From the condition it is known that the leg of a right-angled triangle is 9 cm, and the hypotenuse and the second leg are related as 5: 4.

In order to find the length of the hypotenuse and the second leg, we apply the Pythagorean theorem. She says that the square of the hypotenuse is equal to the sum of the squares of the legs.

Let us denote the similarity coefficient as k and get: 5k – hypotenuse, 4k – leg.

We apply the theorem and get the equation:

(5k) ^ 2 = 9 ^ 2 + (4k) ^ 2;

25k ^ 2 = 81 – 16k ^ 2;

k ^ 2 (25 – 16) = 81;

9k ^ 2 = 81;

k ^ 2 = 9;

k = 3.

So, the hypotenuse is 5 * 3 = 15 cm, and the leg is 4 * 3 = 12 cm.