The sum of the length of a rectangle and the side of a square is 72 meters. If the perimeter of the rectangle is 84 meters and the breadth of the rectangle is 8 meters, then find the side of square (in meters).

Options

A. 48
B. 38
C. 60
D. 30

Answer

To solve the problem step by step, we will follow the information given in the question and derive the required values.

### Step 1: Understand the given information
- The sum of the length of a rectangle (let's denote it as \( l \)) and the side of a square (let's denote it as \( a \)) is 72 meters.
- The perimeter of the rectangle is 84 meters.
- The breadth of the rectangle (denote it as \( b \)) is 8 meters.

### Step 2: Write down the equations
From the information provided, we can formulate the following equations:
1. \( l + a = 72 \) (Equation 1)
2. The formula for the perimeter of a rectangle is \( P = 2(l + b) \). Given that the perimeter is 84 meters, we can write:
\[ 2(l + b) = 84 \]
Dividing both sides by 2 gives:
\[ l + b = 42 \quad \text{(Equation 2)} \]

### Step 3: Substitute the breadth into Equation 2
We know the breadth \( b = 8 \) meters. Substitute this value into Equation 2:
\[ l + 8 = 42 \]
Now, solve for \( l \):
\[ l = 42 - 8 \]
\[ l = 34 \text{ meters} \]

### Step 4: Substitute the length into Equation 1
Now that we have \( l = 34 \) meters, substitute this value into Equation 1 to find \( a \):
\[ 34 + a = 72 \]
Now, solve for \( a \):
\[ a = 72 - 34 \]
\[ a = 38 \text{ meters} \]

### Step 5: Conclusion
The side of the square \( a \) is 38 meters.

### Final Answer
The side of the square is **38 meters**.

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