A rectangular sheet of paper is `15 3/4` cm long and `12 1/2` cm wide. Find its perimeter.

Options

A. `36 1/2`cm
B. `66 1/2`cm
C. `56 1/2`cm
D. `46 1/2`cm

Answer

To find the perimeter of a rectangular sheet of paper, we can use the formula for the perimeter of a rectangle:

**Perimeter (P) = 2 × (Length + Width)**

Given:
- Length = `15 3/4` cm
- Width = `12 1/2` cm

**Step 1: Convert the mixed numbers to improper fractions.**

1. For the length `15 3/4`:
- Convert to improper fraction:
- \( 15 \times 4 + 3 = 60 + 3 = 63 \)
- So, \( 15 3/4 = \frac{63}{4} \) cm

2. For the width `12 1/2`:
- Convert to improper fraction:
- \( 12 \times 2 + 1 = 24 + 1 = 25 \)
- So, \( 12 1/2 = \frac{25}{2} \) cm

**Step 2: Add the length and width.**

- Length + Width = \( \frac{63}{4} + \frac{25}{2} \)

To add these fractions, we need a common denominator. The least common multiple of 4 and 2 is 4.

- Convert \( \frac{25}{2} \) to have a denominator of 4:
- \( \frac{25}{2} = \frac{25 \times 2}{2 \times 2} = \frac{50}{4} \)

Now we can add:
- \( \frac{63}{4} + \frac{50}{4} = \frac{63 + 50}{4} = \frac{113}{4} \)

**Step 3: Calculate the perimeter.**

- Using the perimeter formula:
- \( P = 2 \times (Length + Width) \)
- \( P = 2 \times \frac{113}{4} \)

Multiply:
- \( P = \frac{2 \times 113}{4} = \frac{226}{4} \)

Now simplify:
- \( \frac{226}{4} = 56.5 \) cm or \( 56 \frac{1}{2} \) cm

**Final Answer:**
The perimeter of the rectangular sheet of paper is \( 56 \frac{1}{2} \) cm.

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