The perimeter of a rectangle is 13 cm and its width is `(2) 3/4 cm .` Find its length.

Options

A. `3 11/4`
B. `3 3/4`
C. `3 15/4`
D. `7 31/7`

Explanation

To find the length of the rectangle given its perimeter and width, we can follow these steps:

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

### Step 2: Identify the known values.
From the problem, we know:
- The perimeter \( P = 13 \) cm
- The width \( b = 2 \frac{3}{4} \) cm

### Step 3: Convert the mixed number to an improper fraction.
To make calculations easier, convert the width \( b \) into an improper fraction:
\[ b = 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ cm} \]

### Step 4: Substitute the known values into the perimeter formula.
Substituting the values of \( P \) and \( b \) into the perimeter formula:
\[ 13 = 2 \times (l + \frac{11}{4}) \]

### Step 5: Simplify the equation.
Distributing the 2 on the right side:
\[ 13 = 2l + \frac{11}{2} \]

### Step 6: Eliminate the fraction.
To eliminate the fraction, multiply both sides by 2:
\[ 2 \times 13 = 2 \times (2l + \frac{11}{2}) \]
\[ 26 = 4l + 11 \]

### Step 7: Solve for \( l \).
Now, isolate \( l \) by first subtracting 11 from both sides:
\[ 26 - 11 = 4l \]
\[ 15 = 4l \]
Now, divide both sides by 4:
\[ l = \frac{15}{4} \text{ cm} \]

### Step 8: Convert the improper fraction back to a mixed number.
To convert \( \frac{15}{4} \) into a mixed number:
\[ \frac{15}{4} = 3 \frac{3}{4} \text{ cm} \]

### Final Answer:
The length of the rectangle is \( 3 \frac{3}{4} \) cm.

---