Question

rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 25 ft long and 18 ft wide. if the garde 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 su lude the correct unit in your answer.)

Explanation:

Step1: Analyze the fence structure

The fence consists of two lengths of the rectangle, one width of the rectangle, and the curved part of the semicircle. The diameter of the semicircle is equal to the width of the rectangle (18 ft), so the radius \( r=\frac{18}{2} = 9\) ft. The length of the curved part of the semicircle is half the circumference of a full circle, given by \( C_{semicircle}=\frac{1}{2}\times2\pi r=\pi r\).

Step2: Calculate the length of the semicircular part

Using \( \pi = 3.14\) and \( r = 9\) ft, we get \( C_{semicircle}=3.14\times9=28.26\) ft.

Step3: Calculate the lengths from the rectangle

The rectangle has a length of 25 ft, so two lengths contribute \( 2\times25 = 50\) ft. The width contributing is 18 ft (since one width is where the semicircle is attached, so we don't include that width twice).

Step4: Sum up all the parts

Total fence length \(= 50+18 + 28.26\). First, \( 50+18=68\), then \( 68 + 28.26=96.26\) ft.

Answer:

96.26 feet