A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 27ft long and 20ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Question
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 27ft long and 20ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Solution 1
The question seems to be missing the diagram, but based on the description, we can assume that the diameter of the semicircle is the same as the width of the rectangle, which is 20ft.
To find the total length of the fence, we need to add the perimeter of the rectangle and the circumference of the semicircle.
Step 1: Calculate the perimeter of the rectangle. The formula for the perimeter of a rectangle is 2(length + width). So, the perimeter of the rectangle is 2(27ft + 20ft) = 94ft.
Step 2: Calculate the circumference of the semicircle. The formula for the circumference of a circle is πd, but since we only have a semicircle, we will take half of this. The diameter of the semicircle is 20ft (the same as the width of the rectangle). So, the circumference of the semicircle is 1/2(π*20ft) = 31.4ft.
Step 3: Add the perimeter of the rectangle and the circumference of the semicircle to get the total length of the fence. So, the total length of the fence is 94ft + 31.4ft = 125.4ft.
So, the gardener will need 125.4ft of fence to build around the garden.
Solution 2
The question seems to be missing the diagram, but based on the description, we can assume that the diameter of the semicircle is the same as the width of the rectangle (20ft).
Step 1: Calculate the perimeter of the rectangle. The formula for the perimeter of a rectangle is 2(length + width).
Perimeter of rectangle = 2(27ft + 20ft) = 2(47ft) = 94ft
Step 2: Calculate the circumference of the semicircle. The formula for the circumference of a circle is πd (where d is the diameter), and since we only have a semicircle, we will take half of this value.
Circumference of semicircle = 1/2(πd) = 1/2(3.14 * 20ft) = 31.4ft
Step 3: Add the perimeter of the rectangle and the circumference of the semicircle to get the total length of the fence required.
Total length of fence = Perimeter of rectangle + Circumference of semicircle = 94ft + 31.4ft = 125.4ft
So, the gardener would need 125.4 feet of fence to build around the garden.
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