Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 25 ft long and 17 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 π, and do not round your answer. be sure to include the correct unit in your answer.)

Explanation:

Step1: Calculate the perimeter of the rectangle part

The rectangle has two sides of length \(25\) ft and one side of length \(17\) ft.
\(25 + 25+17\)

Step2: Calculate the circumference of the semicircle

The diameter of the semicircle is \(17\) ft. The formula for the circumference of a semicircle is \(\frac{1}{2}\times\pi\times d\). Using \(\pi = 3.14\) and \(d = 17\) ft, we have \(\frac{1}{2}\times3.14\times17\)

Step3: Sum up the lengths

Add the results from Step1 and Step2.
\((25 + 25+17)+\frac{1}{2}\times3.14\times17\)
\(=67 + 26.69\)
\(=93.69\)

Answer:

\(93.69\) ft