Sides of a parallelogram are in the ratio 5: 4. Its area is 1000 sq. units. Altitude on the greater side is 20 units. Altitude on the smaller side is

Options

A. 30 units
B. 25 units
C. 10 units
D. 15 units

Answer

To solve the problem step by step, we will follow the information given in the question regarding the sides of the parallelogram, its area, and the altitudes.

### Step-by-Step Solution:

1. **Identify the sides of the parallelogram**:
The sides of the parallelogram are in the ratio 5:4. Let's denote the lengths of the sides as:
- Greater side (base) = \(5x\)
- Smaller side (base) = \(4x\)

2. **Use the area of the parallelogram**:
The area \(A\) of a parallelogram is given by the formula:
\[ A = \text{base} \times \text{height} \]
We know the area is \(1000 \, \text{sq. units}\) and the altitude (height) on the greater side (base) is \(20 \, \text{units}\). Thus, we can write:
\[ 1000 = (5x) \times 20 \]

3. **Solve for \(x\)**:
Rearranging the equation gives:
\[ 1000 = 100x \]
Dividing both sides by \(100\):
\[ x = \frac{1000}{100} = 10 \]

4. **Find the lengths of the sides**:
Now that we have \(x\), we can find the lengths of the sides:
- Greater side = \(5x = 5 \times 10 = 50 \, \text{units}\)
- Smaller side = \(4x = 4 \times 10 = 40 \, \text{units}\)

5. **Use the area to find the altitude on the smaller side**:
We can now use the area formula again to find the altitude on the smaller side. The area can also be expressed as:
\[ A = \text{base} \times \text{height} \]
For the smaller side:
\[ 1000 = (4x) \times h \]
Substituting \(4x\) with \(40\):
\[ 1000 = 40 \times h \]

6. **Solve for \(h\)**:
Rearranging gives:
\[ h = \frac{1000}{40} = 25 \, \text{units} \]

### Final Answer:
The altitude on the smaller side is \(25 \, \text{units}\).

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