A rose garden is designed by joining a rectangle and a semicircle, as shown below. The rectangle is 29ft long and 17ft 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 pi, and do not round your answer. Be sure to include the correct unit in your answer.)
Which side is the semicircle on?
To find the total length of the fence required, we need to calculate the perimeter of the garden.
1. Perimeter of the rectangle: The rectangle has a length of 29 ft and a width of 17 ft. The formula to find the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width.
So, P_rectangle = 2(29 ft + 17 ft) = 2(46 ft) = 92 ft.
2. Perimeter of the semicircle: The semicircle is formed by joining the straight sides of the rectangle. The formula to find the perimeter of a semicircle is P = πr + 2r, where r is the radius of the semicircle.
To find the radius, we need to find the diameter first. The diameter is equal to the width of the rectangle, which is 17 ft. So, the radius is half the diameter: r = 17 ft / 2 = 8.5 ft.
Now, let's find the perimeter of the semicircle: P_semicircle = π(8.5 ft) + 2(8.5 ft) = 8.5π ft + 17 ft.
3. Total perimeter: We need to sum the perimeters of the rectangle and the semicircle to find the total perimeter of the garden:
Total perimeter = P_rectangle + P_semicircle
= 92 ft + (8.5π ft + 17 ft)
= 109 ft + 8.5π ft.
So, the total length of fence required to enclose the rose garden is 109 ft + 8.5π ft.
To find the amount of fence required for the rose garden, we need to calculate the perimeter of the garden, which consists of the rectangle and the semicircle.
First, let's calculate the perimeter of the rectangle. The rectangle has a length of 29ft and a width of 17ft.
To find the perimeter of a rectangle, we use the formula: perimeter = 2(length + width)
So, for the rectangle: perimeter = 2(29ft + 17ft) = 2(46ft) = 92ft.
Next, let's calculate the perimeter of the semicircle. The semicircle is formed by the curved part of the garden.
The formula to find the circumference of a semicircle is: circumference = (pi * r) + 2r, where r is the radius of the semicircle.
In this case, the width of the rectangle (17ft) is equal to the diameter of the semicircle since the semicircle's diameter is equal to the rectangle's width. So, the radius (r) is half the width, which is 17ft / 2 = 8.5ft.
Now, let's calculate the circumference of the semicircle:
circumference = (3.14 * 8.5ft) + 2(8.5ft) = 26.69ft + 17ft = 43.69ft.
Finally, to find the total amount of fence required, we add the perimeters of the rectangle and the semicircle:
total fence required = rectangle perimeter + semicircle perimeter = 92ft + 43.69ft = 135.69ft.
Therefore, 135.69 feet of fence are required to enclose the rose garden.