Two sides of a parallelogram are in the ratio `4 : 3`. If its perimeter is `56 cm`, find the length and breadth .

Options

A. `16 cm, 14 cm`
B. `16 cm, 10 cm`
C. `16 cm, 12 cm`
D. `15 cm, 12 cm`

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the Problem
We are given that the sides of a parallelogram are in the ratio of 4:3, and the perimeter is 56 cm. We need to find the lengths of the two sides.

### Step 2: Define the Variables
Let the lengths of the two sides of the parallelogram be:
- Length (longer side) = 4x
- Breadth (shorter side) = 3x

### Step 3: Write the Perimeter Formula
The perimeter (P) of a parallelogram is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the values we defined:
\[ P = 2 \times (4x + 3x) \]

### Step 4: Simplify the Perimeter Expression
Now, simplify the expression:
\[ P = 2 \times (7x) = 14x \]

### Step 5: Set Up the Equation
We know from the problem that the perimeter is 56 cm, so we can set up the equation:
\[ 14x = 56 \]

### Step 6: Solve for x
To find x, divide both sides of the equation by 14:
\[ x = \frac{56}{14} \]
\[ x = 4 \]

### Step 7: Calculate the Length and Breadth
Now that we have the value of x, we can find the lengths of the sides:
- Length = \( 4x = 4 \times 4 = 16 \) cm
- Breadth = \( 3x = 3 \times 4 = 12 \) cm

### Step 8: Conclusion
The lengths of the sides of the parallelogram are:
- Length = 16 cm
- Breadth = 12 cm