A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is $29 \mathrm{ft}$ long and $18 \mathrm{ft}$ wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? $\newline$ 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. $\newline$ $\square$ $f t$ $\newline$ $f t^{2}$ $\newline$ $\mathrm{ft}^{3}$ $\newline$ $29 \mathrm{ft}$ $\newline$ Save For Later $\newline$ Submit Assignment $\newline$ Check

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Q. A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is

29 \mathrm{ft}

long and

18 \mathrm{ft}

wide. If the gardener wants to build a fence around the garden, how many feet of fence are required?

\newline

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.

\newline

\square

f t

\newline

f t^{2}

\newline

\mathrm{ft}^{3}

\newline

29 \mathrm{ft}

\newline

Save For Later

\newline

Submit Assignment

\newline

Check

Calculate Perimeter of Rectangle: Calculate the perimeter of the rectangle part of the garden. $\newline$ Perimeter of rectangle = $2(\text{length} + \text{width})$ $\newline$ = $2(29\,\text{ft} + 18\,\text{ft})$ $\newline$ = $2(47\,\text{ft})$ $\newline$ = $94\,\text{ft}$
Find Diameter of Semicircle: Find the diameter of the semicircle, which is the same as the width of the rectangle. $\newline$ Diameter of semicircle = $18\,\text{ft}$
Calculate Circumference of Semicircle: Calculate the circumference of the semicircle. $\newline$ Circumference of semicircle = $\pi(\text{diameter})$ $\newline$ But since it's a semicircle, we take half of the circumference. $\newline$ Circumference of semicircle = $\frac{1}{2} \times \pi \times 18\text{ft}$ $\newline$ = $\frac{1}{2} \times \pi \times 18$ $\newline$ = $9\pi \text{ft}$
Add Perimeter and Circumference: Add the perimeter of the rectangle and the circumference of the semicircle to get the total length of the fence needed. $\newline$ Total length of fence = Perimeter of rectangle + Circumference of semicircle $\newline$ = $94\text{ft} + 9\pi \text{ft}$ $\newline$ = $94 + 9(3.14) \text{ft}$ $\newline$ = $94 + 28.26 \text{ft}$ $\newline$ = $122.26 \text{ft}$