Questions: You are building a fence around your vegetable garden in your backyard. If the garden is 12′ 8″ long and 4′ 6″ wide, what is the total length of fencing you will need?

You are building a fence around your vegetable garden in your backyard. If the garden is 12′ 8″ long and 4′ 6″ wide, what is the total length of fencing you will need?

Transcript text: You are building a fence around your vegetable garden in your backyard. If the garden is $12^{\prime} 8^{\prime \prime}$ long and $4^{\prime} 6^{\prime \prime}$ wide, what is the total length of fencing you will need?

Solution

Solution Steps

Step 1: Convert Measurements

The length of the garden is given as $12^{\prime} 8^{\prime \prime}$. Converting this to feet: \[ \text{length} = 12 + \frac{8}{12} = 12.6667 \text{ feet} \] The width of the garden is given as $4^{\prime} 6^{\prime \prime}$. Converting this to feet: \[ \text{width} = 4 + \frac{6}{12} = 4.5 \text{ feet} \]

Step 2: Calculate the Perimeter

The perimeter $P$ of a rectangle is calculated using the formula: \[ P = 2 \times (\text{length} + \text{width}) \] Substituting the values we found: \[ P = 2 \times (12.6667 + 4.5) = 2 \times 17.1667 = 34.3333 \text{ feet} \]