Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 22 ft long and 15 ft wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? do not round any intermediate computations. round your final answer to the nearest hundredth and be sure to include the correct unit. if necessary, refer to the list of geometry formulas.

Explanation:

Step1: Calculate the length of the straight - side parts of the fence

The rectangle has two lengths of \(22\) ft and one width of \(15\) ft (the other width is adjacent to the semicircle and not part of the fence).
So the sum of the straight - side lengths is \(22 + 22+15\).

$$22 + 22+15=59$$

Step2: Calculate the length of the semicircular part of the fence

The formula for the circumference of a full - circle is \(C = \pi d\), where \(d\) is the diameter. For a semicircle, the length \(L=\frac{\pi d}{2}\). Given \(d = 15\) ft.

$$L=\frac{\pi\times15}{2}=\frac{15\pi}{2}$$

Step3: Calculate the total length of the fence

The total length \(T\) of the fence is the sum of the straight - side lengths and the semicircular length.

$$T=59+\frac{15\pi}{2}$$

Substitute \(\pi = 3.14159265\)

$$T=59+\frac{15\times3.14159265}{2}=59 + 23.5619449$$

$$T=82.5619449\approx82.56$$

Answer:

\(82.56\) ft