The area of a right angled triangle is 10 sq cm. If its perpendicular is equal to 20 cm, find its base.

Options

A. 1 cm
B. 4 cm
C. 3 cm
D. 2 cm

Answer

To find the base of a right-angled triangle given its area and perpendicular height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Area**:
The area \( A \) of a right-angled triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{perpendicular} \]

2. **Identify the Given Values**:
From the problem, we know:
- Area \( A = 10 \, \text{sq cm} \)
- Perpendicular (height) \( h = 20 \, \text{cm} \)

3. **Substitute the Known Values into the Formula**:
Plugging the known values into the area formula:
\[ 10 = \frac{1}{2} \times \text{base} \times 20 \]

4. **Simplify the Equation**:
First, multiply both sides by 2 to eliminate the fraction:
\[ 20 = \text{base} \times 20 \]

5. **Solve for the Base**:
Now, divide both sides by 20 to isolate the base:
\[ \text{base} = \frac{20}{20} = 1 \, \text{cm} \]

6. **Conclusion**:
The base of the right-angled triangle is \( 1 \, \text{cm} \).

### Final Answer:
The base of the right-angled triangle is \( 1 \, \text{cm} \).