The legs of a right-angled triangle are 3: 4, and the hypotenuse is 5 cm. Find the perimeter of the triangle.

In the event that the legs of a right-angled triangle are related to each other as 3: 4, we get the Egyptian triangle.

Let’s write the value of one part as x.

So the legs will be equal to 3 * x and 4 * x.

By the Pythagorean theorem, we get:

5 ^ 2 = (3 * x) ^ 2 + (4 * x) ^ 2.

25 = 9 * x ^ 2 + 16 * x ^ 2.

25 = 25 * x ^ 2.

x = 1 cm.

So one part is equal to 1 cm.

The perimeter of a triangle is equal to the sum of all its sides.

in this case, we get:

P = 3 * 1 + 4 * 1 + 5 = 3 + 4 + 5 = 12 cm.

Answer: The perimeter of the triangle is 12 cm.