The breadth of a rectangular bed sheet is 5 m more than half the length of the bed sheet. What is the perimeter of the bed sheet, if the length is x m?

Options

A. `(3x+12)m`
B. `2(x+5)m`
C. `(3x+10)m`
D. `(4x+12)m`

Answer

To solve the problem step by step, we will first define the variables and then calculate the perimeter of the rectangular bed sheet.

### Step 1: Define the Length
Let the length of the bed sheet be \( x \) meters.

### Step 2: Define the Breadth
According to the problem, the breadth of the bed sheet is 5 meters more than half the length.
- Half of the length is \( \frac{x}{2} \).
- Therefore, the breadth \( b \) can be expressed as:
\[ b = \frac{x}{2} + 5 \]

### Step 3: Calculate the Perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
Substituting the values we have:
\[ P = 2 \times \left(x + \left(\frac{x}{2} + 5\right)\right) \]

### Step 4: Simplify the Expression
Now, simplify the expression inside the parentheses:
\[ P = 2 \times \left(x + \frac{x}{2} + 5\right) \]
Combine \( x \) and \( \frac{x}{2} \):
\[ x = \frac{2x}{2} \quad \text{(to have a common denominator)} \]
So,
\[ P = 2 \times \left(\frac{2x}{2} + \frac{x}{2} + 5\right) = 2 \times \left(\frac{3x}{2} + 5\right) \]

### Step 5: Distribute the 2
Now distribute the 2:
\[ P = 2 \times \frac{3x}{2} + 2 \times 5 = 3x + 10 \]

### Final Answer
Thus, the perimeter of the bed sheet is:
\[ \boxed{3x + 10 \text{ meters}} \]