To calculate the perimeter of the given right triangle, we need to find the length of the hypotenuse and sum it with the other two sides.

Information from the diagram:

• One leg (height) is $9 \, \text{cm}$,
• The other leg is $12 \, \text{cm} - 2 \, \text{cm} = 10 \, \text{cm}$ (subtracting the shorter segment on the bottom).

Step 1: Use the Pythagorean theorem to find the hypotenuse.

$\text{Hypotenuse}^2 = (\text{leg}_1)^2 + (\text{leg}_2)^2$ $\text{Hypotenuse}^2 = 9^2 + 10^2 = 81 + 100 = 181$ $\text{Hypotenuse} = \sqrt{181} \approx 13.5 \, \text{cm}$

Step 2: Calculate the perimeter.

The perimeter of the triangle is the sum of the lengths of all sides: $\text{Perimeter} = 9 \, \text{cm} + 10 \, \text{cm} + 13.5 \, \text{cm} = 32.5 \, \text{cm}$

Thus, the perimeter of the triangle is 32.5 cm to 1 decimal place.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What is the area of the triangle?
2. How would the perimeter change if one of the legs increased by 2 cm?
3. Can the triangle be classified as isosceles or scalene?
4. How would you calculate the perimeter if the hypotenuse was provided instead of one of the legs?
5. How is the Pythagorean theorem used in three-dimensional shapes?

Tip: Always check if a triangle is a right triangle before applying the Pythagorean theorem.