To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula can be expressed as: c² = a² + b².
In this case, we have the lengths of the two legs:
- a = 9 cm
- b = 12 cm
Substituting these values into the formula gives us:
c² = 9² + 12²
Calculating the squares, we get:
- 9² = 81
- 12² = 144
Now, we add these results:
c² = 81 + 144 = 225
Next, to find the length of the hypotenuse, we take the square root of 225:
c = √225 = 15 cm
Therefore, the length of the hypotenuse is 15 cm.