# Given a right-angled triangle. It is known that the lengths of the legs are related

**Given a right-angled triangle. It is known that the lengths of the legs are related to each other as 3: 4. Find the hypotenuse of this triangle if the smaller leg is 6 cm.**

We are given a right-angled triangle. It is known from the condition that the lengths of the legs are related to each other as 3: 4. The smaller leg is 6 cm. We need to find the length of the hypotenuse.

To find the length of the hypotenuse, we will use the Pythagorean theorem, it says that the square of the hypotenuse is equal to the sum of the squares of the legs.

Let’s find the value of the second leg. We are given a 3: 4 leg ratio.

The smaller leg of 6 cm is also known, let’s find the coefficient of similarity.

3x = 6;

x = 2.

Then the second leg is 4 * 2 = 8 cm.

We are looking for the hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2;

c ^ 2 = 6 ^ 2 + 8 ^ 2;

c ^ 2 = 36 + 64;

c ^ 2 = 100;

c = 10 cm hypotenuse of the triangle.