The hypotenuse of a right angled triangle is `45` cm long. If one of the legs of this triangle is `36` cm, then find the length of other leg.

Answer

To find the length of the other leg of a right-angled triangle when the hypotenuse and one leg are given, we can use the Pythagorean theorem. The theorem states that in a right-angled 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 legs (a and b). The formula is:

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

Where:
- \( c \) is the hypotenuse,
- \( a \) and \( b \) are the legs of the triangle.

### Step-by-Step Solution:

1. **Identify the given values:**
- Hypotenuse \( c = 45 \) cm
- One leg \( a = 36 \) cm
- We need to find the length of the other leg \( b \).

2. **Apply the Pythagorean theorem:**
\[ c^2 = a^2 + b^2 \]
Substituting the known values:
\[ 45^2 = 36^2 + b^2 \]

3. **Calculate \( 45^2 \) and \( 36^2 \):**
\[ 45^2 = 2025 \]
\[ 36^2 = 1296 \]

4. **Substitute these values into the equation:**
\[ 2025 = 1296 + b^2 \]

5. **Rearrange the equation to solve for \( b^2 \):**
\[ b^2 = 2025 - 1296 \]

6. **Calculate \( 2025 - 1296 \):**
\[ 2025 - 1296 = 729 \]
So, \( b^2 = 729 \).

7. **Take the square root of both sides to find \( b \):**
\[ b = \sqrt{729} \]

8. **Calculate \( \sqrt{729} \):**
\[ b = 27 \]

### Conclusion:
The length of the other leg of the triangle is \( 27 \) cm.

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