Final answer:
To calculate the amount of fencing needed for the rose garden, the perimeter of the rectangle and the circumference of the semicircle are added. With dimensions given, the fencing required is 90.42 feet, which does not match the options provided.
Step-by-step explanation:
The question involves determining the total length of fencing required to enclose a rose garden that is shaped by joining a rectangle with a semicircle. The dimensions given for the rectangle are 22 ft in length and 13 ft in width. To find the total fence length, we must calculate the perimeter of the rectangle and the circumference of the semicircle and then add them together.
For the rectangle, we have two sides of 22 ft and two sides of 13 ft, so the rectangular perimeter (Prectangle) is 2(22 ft) + 2(13 ft) = 44 ft + 26 ft = 70 ft. For the semicircle, we first need the diameter to find the circumference. Since one side of the rectangle will act as the diameter for our semicircle, the diameter (D) is the same as the width of the rectangle, which is 13 ft.
The circumference of a full circle (Ccircle) is πD, so for a semicircle, it is half of that: Csemicircle = (πD)/2. Using the value π = 3.14, we get Csemicircle = (3.14 × 13 ft)/2 = 20.42 ft. Now, we must add the perimeter of the rectangle to the circumference of the semicircle to get the total fencing needed: Total fencing = Prectangle + Csemicircle = 70 ft + 20.42 ft = 90.42 ft.
Thus, the gardener will require 90.42 feet of fencing to enclose the garden. This does not match any of the options given (A, B, C, or D), suggesting a typo or error in the question's options.