Question

A rose garden is formed joining a rectangle and semicircle as shown below. The rectangle is 26ft long and 16ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required. Use the 3.14 for pie and do not round your answer. Be sure to include the correct unit in your answer

Answer 1

To calculate the total length of the fence required for the rose garden, we need to add the perimeter of the rectangular part and the circumference of the semicircular part.

### Step 1: Calculate the perimeter of the rectangle
The rectangle has a length of 26 ft and a width of 16 ft.

The formula for the perimeter of a rectangle is:
\[
P = 2 \times \text{length} + 2 \times \text{width}
\]

However, since one of the lengths of the rectangle is joined with the semicircle, we only take into account the three remaining sides:
\[
\text{Perimeter of rectangle} = 2 \times \text{width} + \text{length} = 2 \times 16 + 26 = 32 + 26 = 58 \text{ ft}
\]

### Step 2: Calculate the circumference of the semicircle
The radius of the semicircle is half the width of the rectangle:
\[
\text{Radius} = \frac{\text{width}}{2} = \frac{16}{2} = 8 \text{ ft}
\]

The formula for the circumference of a full circle is:
\[
C = 2 \pi r
\]
For a semicircle, we take half of this:
\[
\text{Circumference of semicircle} = \frac{1}{2} \times 2 \pi r = \pi r
\]
Substituting the value for the radius:
\[
\text{Circumference of semicircle} = 3.14 \times 8 = 25.12 \text{ ft}
\]

### Step 3: Add the lengths together
Now we add the perimeter of the rectangle and the circumference of the semicircle:
\[
\text{Total fence length} = \text{Perimeter of rectangle} + \text{Circumference of semicircle} = 58 + 25.12 = 83.12 \text{ ft}
\]

### Final Answer
Thus, the total length of the fence required is:
\[
\boxed{83.12 \text{ ft}}
\]