Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 23 ft long and 15 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 1, and do not round your answer. Be sure to include the correct unit inyour answer.)15 ft23ft

Answer 1

`99.55ft`

Step-by-step explanation:

We were given the following information:

A rose garden is formed by joining a rectangle and a semicircle, as shown below:

Rectangle: Length = 23 feet, Width = 15 feet

Semicircle: Diameter = 15 feet; radius = Diameter/2 = 15/2 = 7.5 feet

Pi = 3.14

We will calculate the perimeter of the garden as shown below:

`\begin{gathered} Perimeter_(garden)=Perimeter_(rectangle)+Perimeter_(semicircle) \\ Perimeter_(rectangle)=2(length+width)=2(23+15)=2(38)=76ft \\ Perimeter_(semicircle)\Rightarrow(1)/(2)Perimeter_(circle)\Rightarrow(1)/(2)*2\pi r=\pi r=3.14*7.5=23.55ft \\ Perimeter_(garden)=76+23.55=99.55 \\ Perimeter_(garden)=99.55ft \\ \\ \therefore Perimeter_(garden)=99.55ft \end{gathered}`

Therefore, the gardener will need to build a fence of length 99.55 feet