Answer:
[tex]99.55ft[/tex]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:
[tex]\begin{gathered} Perimeter_{garden}=Perimeter_{rectangle}+Perimeter_{semicircle} \\ Perimeter_{rectangle}=2(length+width)=2(23+15)=2(38)=76ft \\ Perimeter_{semicircle}\Rightarrow\frac{1}{2}Perimeter_{circle}\Rightarrow\frac{1}{2}\times2\pi r=\pi r=3.14\times7.5=23.55ft \\ Perimeter_{garden}=76+23.55=99.55 \\ Perimeter_{garden}=99.55ft \\ \\ \therefore Perimeter_{garden}=99.55ft \end{gathered}[/tex]Therefore, the gardener will need to build a fence of length 99.55 feet
