Find the perimeter of a triangle, whose legs are equal: 9cm, 12cm.

We need to find the perimeter of a right-angled triangle, whose legs are respectively 9 cm and 12 cm.

To find the perimeter of a triangle, we will apply the formula:

P = a + b + c (the perimeter of a triangle is the sum of the lengths of its sides).

First of all, we need to find the length of the hypotenuse of the triangle. For this we apply the Pythagorean theorem, which says that the sum of the squares of the legs is equal to the square of the hypotenuse:

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

c = √ (a ^ 2 + b ^ 2) = √ (12 ^ 2 + 9 ^ 2) = √ (144 + 81) = √225 = 15 cm.

P = 9 + 12 + 15 = 36 cm.