The area of a parallelogram ABCD is `300 cm^(2)` , The distance between AB and CD is 20cm, and the distance between BC and AD is 30cm. What is the perimeter (in cm) of the parallelogram ?

Options

A. 60
B. 50
C. 40
D. 100

Answer

To find the perimeter of the parallelogram ABCD, we can follow these steps:

### Step 1: Understand the Area Formula
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
In this case, we have two bases and their corresponding heights.

### Step 2: Use the Given Area and Height
We know the area of the parallelogram is \( 300 \, \text{cm}^2 \). We can use the height between the bases AB and CD, which is \( 20 \, \text{cm} \), to find the length of base AB (or CD).

Using the formula:
\[ 300 = \text{base} \times 20 \]
Let the base be \( b_1 \):
\[ b_1 = \frac{300}{20} = 15 \, \text{cm} \]

### Step 3: Calculate the Other Base
Next, we can use the height between the sides BC and AD, which is \( 30 \, \text{cm} \), to find the length of base BC (or AD).

Using the formula:
\[ 300 = \text{base} \times 30 \]
Let the base be \( b_2 \):
\[ b_2 = \frac{300}{30} = 10 \, \text{cm} \]

### Step 4: Determine the Lengths of All Sides
In a parallelogram, opposite sides are equal. Therefore:
- Length of AB = Length of CD = \( 15 \, \text{cm} \)
- Length of BC = Length of AD = \( 10 \, \text{cm} \)

### Step 5: Calculate the Perimeter
The perimeter \( P \) of a parallelogram is given by:
\[ P = 2 \times (\text{length of one pair of opposite sides} + \text{length of the other pair of opposite sides}) \]
Substituting the values:
\[ P = 2 \times (15 + 10) = 2 \times 25 = 50 \, \text{cm} \]

### Final Answer
The perimeter of the parallelogram ABCD is \( 50 \, \text{cm} \).

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