Find the perimeter of a right-angled triangle with legs AC = 9 and BC = 12, angle ACB = 90 degrees.

From the condition it is known that a right-angled triangle with legs AC = 9 and BC = 12 and angle ACB = 90 °. And we need to find the perimeter of a right-angled triangle.
The perimeter is the sum of the lengths of all sides of the triangle:
P = a + b + c;
We need to find the length of the hypotenuse, and then add the sum of the lengths of the three sides. To find the hypotenuse, we apply the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
c = √ (a ^ 2 + b ^ 2).
Substitute the values and calculate:
c = √ (9 ^ 2 + 12 ^ 2) = √ (81 + 144) = √225 = 15.
We are looking for a perimeter:
P = 9 + 12 + 15 = 36.