Area of a parellogram is `800 cm^(2)` and ratio of length and breadth is 5 : 4 . If distance b/w bigger side is 20 cm . Find the distance between smaller side.

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the variables
Let the length of the parallelogram be \(5x\) and the breadth be \(4x\), based on the given ratio of \(5:4\).

### Step 2: Use the area formula
The area \(A\) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
Given that the area is \(800 \, \text{cm}^2\) and the distance (height) between the longer side (base) is \(20 \, \text{cm}\), we can use this information to find \(x\).

### Step 3: Calculate the area using the longer side
Using the longer side as the base:
\[ A = \text{base} \times \text{height} = 5x \times 20 \]
Setting this equal to the area:
\[ 5x \times 20 = 800 \]
\[ 100x = 800 \]
\[ x = \frac{800}{100} = 8 \]

### Step 4: Calculate the dimensions
Now that we have \(x\), we can find the dimensions:
- Length \(L = 5x = 5 \times 8 = 40 \, \text{cm}\)
- Breadth \(B = 4x = 4 \times 8 = 32 \, \text{cm}\)

### Step 5: Find the distance between the smaller side
Now we need to find the distance (height) between the smaller side (base). Using the breadth as the base:
\[ A = \text{base} \times \text{height} = 4x \times h \]
Setting this equal to the area:
\[ 4x \times h = 800 \]
Substituting \(x = 8\):
\[ 4 \times 8 \times h = 800 \]
\[ 32h = 800 \]
\[ h = \frac{800}{32} = 25 \, \text{cm} \]

### Final Answer
The distance between the smaller side is \(25 \, \text{cm}\).

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