A rectangle is 8 cm long and 5 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. 

Options

A. 15 cm
B. 14.5 cm
C. 0.5 cm
D. 9 cm

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the original perimeter of the rectangle.
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times (l + b) \]
where \( l \) is the length and \( b \) is the width.

Given:
- Length \( l = 8 \) cm
- Width \( b = 5 \) cm

Calculating the original perimeter:
\[ P = 2 \times (8 + 5) \]
\[ P = 2 \times 13 \]
\[ P = 26 \text{ cm} \]

### Step 2: Determine the new dimensions after increasing each side by \( x \) cm.
When each side is increased by \( x \) cm:
- New length \( l' = 8 + x \)
- New width \( b' = 5 + x \)

### Step 3: Calculate the new perimeter after the sides are increased.
Using the new dimensions, the new perimeter \( P' \) is:
\[ P' = 2 \times (l' + b') \]
Substituting the new dimensions:
\[ P' = 2 \times ((8 + x) + (5 + x)) \]
\[ P' = 2 \times (13 + 2x) \]
\[ P' = 26 + 4x \]

### Step 4: Set the new perimeter equal to double the original perimeter.
According to the problem, the new perimeter is double the original perimeter:
\[ P' = 2 \times P \]
Substituting the values:
\[ 26 + 4x = 2 \times 26 \]
\[ 26 + 4x = 52 \]

### Step 5: Solve for \( x \).
Now, we will isolate \( x \):
1. Subtract 26 from both sides:
\[ 4x = 52 - 26 \]
\[ 4x = 26 \]

2. Divide both sides by 4:
\[ x = \frac{26}{4} \]
\[ x = 6.5 \text{ cm} \]

### Conclusion:
The value of \( x \) is \( 6.5 \) cm. Therefore, the perimeter of the rectangle will double when each of its sides is increased by \( 6.5 \) cm.

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