One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 13 cm.

One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 13 cm. Find the second leg and the perimeter of the triangle.

Let’s find what the second leg of this right-angled triangle is equal to.

According to the condition of the problem, one of the legs of this right-angled triangle is 12 cm, and the hypotenuse of this triangle is 13 cm, therefore, using the Pythagorean theorem, we can find the second leg of this triangle:

√ (13 ^ 2 – 12 ^ 2) = √ (169 – 144) = √25 = 5.

Knowing the lengths of all three sides of a given triangle, we can find the perimeter P of this triangle:

P = 5 + 12 + 13 = 17 + 13 = 30.

Answer: the second leg is 5, the perimeter of the triangle is 30.