Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 31 ft long and 24 ft 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 , and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

Step-by-step explanation:

First, find the perimeter of the rectangle;

1) perimeter = 2length + 2 width

2) 2(31) + 2 (24) = 110ft

Second, find the circumference of the circle;

1) C = 2πr

2) Since the rectangle is joined to the semicircle, we can assume the diameter is equal the width (or length) of the rectangle. The radius (r) is half of the diameter. (length: r = 15.5 or width: r = 12)

So, C = 2(3.14)(15.5) = 97.32ft

or

C =  2(3.14)(12) = 75.36ft

Since it is a semicircle, we only need half of its circumference.

97.32 / 2 = 48.66

75.36 / 2 = 37.68

Finally, we are going to add up our values;

1) If the semicircle is on the length of the rectangle (remember to subtract the length of width that semicircle attaches to because we won't need fencing there)

(110-31) + 48.66 = 127.66ft

2) If the semicircle is on the width of the rectangle (remember to subtract the length of width that semicircle attaches to because we won't need fencing there)

(110-24) + 37.68 = 123.68ft