The area of a right-angled triangle is 54 sg. cm. If one of the two perpendicular sides is 9 cm, find the other.

Answer

To find the other perpendicular side of the right-angled triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Area of a Triangle:**
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

2. **Identify the Given Values:**
- Area \( A = 54 \, \text{cm}^2 \)
- One perpendicular side (height) \( = 9 \, \text{cm} \)

3. **Set Up the Equation:**
Let the other perpendicular side (base) be \( b \). Using the area formula:
\[ 54 = \frac{1}{2} \times b \times 9 \]

4. **Multiply Both Sides by 2 to Eliminate the Fraction:**
\[ 2 \times 54 = b \times 9 \]
\[ 108 = b \times 9 \]

5. **Solve for \( b \):**
Divide both sides by 9:
\[ b = \frac{108}{9} \]
\[ b = 12 \, \text{cm} \]

6. **Conclusion:**
The other perpendicular side of the triangle is \( 12 \, \text{cm} \).