The difference between the length and the breadth of a rectangle is 7 Cms and the perimeter of the rectangle is 50 Cms What is the area of the rectangle ?

Options

A. 144 Sq Cms
B. 154 Sq Cms
C. 288 Sq Cms
D. 216 Sq Cms

Answer

To solve the problem step by step, we need to find the length and breadth of the rectangle using the given information and then calculate the area.

### Step 1: Set up the equations
Let the length of the rectangle be \( L \) cm and the breadth be \( B \) cm. We know from the problem that:
1. The difference between the length and breadth is 7 cm:
\[ L - B = 7 \quad \text{(Equation 1)} \]
2. The perimeter of the rectangle is 50 cm:
\[ P = 2(L + B) = 50 \quad \text{(Equation 2)} \]

### Step 2: Simplify the perimeter equation
From Equation 2, we can simplify it:
\[ L + B = \frac{50}{2} = 25 \quad \text{(Equation 3)} \]

### Step 3: Solve the system of equations
Now we have two equations:
1. \( L - B = 7 \) (Equation 1)
2. \( L + B = 25 \) (Equation 3)

We can solve these equations simultaneously.

### Step 4: Add the two equations
Adding Equation 1 and Equation 3:
\[ (L - B) + (L + B) = 7 + 25 \]
This simplifies to:
\[ 2L = 32 \]
So, we find:
\[ L = \frac{32}{2} = 16 \quad \text{(Length)} \]

### Step 5: Substitute to find breadth
Now, substitute \( L = 16 \) into Equation 1 to find \( B \):
\[ 16 - B = 7 \]
Rearranging gives:
\[ B = 16 - 7 = 9 \quad \text{(Breadth)} \]

### Step 6: Calculate the area
The area \( A \) of the rectangle is given by:
\[ A = L \times B = 16 \times 9 \]
Calculating this gives:
\[ A = 144 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is \( 144 \text{ cm}^2 \).

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