If the ratio of altitude and area of the parallelogram is 2:11 then find the length of the base of parallelogram.

Answer

To solve the problem, we need to find the length of the base of a parallelogram given the ratio of its altitude to its area.

### Step-by-Step Solution:

1. **Understand the Given Ratio**:
We are given that the ratio of the altitude (h) to the area (A) of the parallelogram is 2:11. This can be expressed mathematically as:
\[ \frac{h}{A} = \frac{2}{11} \]

2. **Express the Area of the Parallelogram**:
The area (A) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} = b \times h \]
where \( b \) is the length of the base and \( h \) is the height (altitude).

3. **Rearranging the Ratio**:
From the ratio \(\frac{h}{A} = \frac{2}{11}\), we can express the area in terms of the altitude:
\[ A = \frac{11}{2} h \]

4. **Substituting the Area into the Area Formula**:
Now, substitute the expression for area \( A \) into the area formula:
\[ \frac{11}{2} h = b \times h \]

5. **Solving for the Base (b)**:
We can solve for \( b \) by dividing both sides by \( h \) (assuming \( h \neq 0 \)):
\[ b = \frac{11}{2} \]

6. **Conclusion**:
Therefore, the length of the base of the parallelogram is:
\[ b = \frac{11}{2} \text{ units} \quad \text{or} \quad 5.5 \text{ units} \]