Find the length of the hypotenuse of a rigt triangle,the other two sides of which measure 9 cm and 12cm

Options

A. `16 cm`
B. `15cm`
C. `17cm`
D. `18cm`

Answer

To find the length of the hypotenuse of a right triangle with the other two sides measuring 9 cm and 12 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is given as:

\[ c^2 = a^2 + b^2 \]

### Step-by-step Solution:

1. **Identify the sides of the triangle**:
- Let \( a = 9 \) cm (one side)
- Let \( b = 12 \) cm (the other side)

2. **Apply the Pythagorean theorem**:
- According to the theorem, we have:
\[ c^2 = a^2 + b^2 \]

3. **Substitute the values of a and b into the equation**:
\[ c^2 = 9^2 + 12^2 \]

4. **Calculate \( 9^2 \) and \( 12^2 \)**:
- \( 9^2 = 81 \)
- \( 12^2 = 144 \)

5. **Add the squares**:
\[ c^2 = 81 + 144 \]
\[ c^2 = 225 \]

6. **Take the square root to find c**:
\[ c = \sqrt{225} \]
\[ c = 15 \text{ cm} \]

### Final Answer:
The length of the hypotenuse is **15 cm**.

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