In the diagram, a garden is enclosed by six straight fences. If the area of the garden is $97 \mathrm{~m}^{2}$, what is the length of the fence around the garden?
(A) $48 \mathrm{~m}$
(B) $47 \mathrm{~m}$
(C) $40 \mathrm{~m}$
(D) $38 \mathrm{~m}$
(E) $37 \mathrm{~m}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-075.jpg?height=439&width=401&top_left_y=1645&top_left_x=1293)
We extend the short horizontal side, $R S$, to the left until it reaches the long vertical side.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-128.jpg?height=471&width=442&top_left_y=1128&top_left_x=901)

Since $P Q R X$ has three right angles, then it must have a fourth right angle and so must be a rectangle.

Since $P Q=Q R$, then $P Q R X$ is in fact a square.

Since the exterior angle at $S$ is a right angle, then $X S T U$ is also a rectangle.

Since $X S T U$ is $2 \mathrm{~m}$ by $8 \mathrm{~m}$, then its area is $2 \times 8=16 \mathrm{~m}^{2}$.

Since the area of the whole garden is $97 \mathrm{~m}^{2}$, then the area of $P Q R X$ is $97-16=81 \mathrm{~m}^{2}$.

Since $P Q R X$ is a square, then its side length is $\sqrt{81}=9 \mathrm{~m}$.

Therefore, $P Q=Q R=R X=X P=9 \mathrm{~m}$.

Since $X S T U$ is a rectangle, then $X S=U T=8 \mathrm{~m}$ and $X U=S T=2 \mathrm{~m}$.

Therefore, $P U=P X+X U=9+2=11 \mathrm{~m}$ and $S R=X R-X S=9-8=1 \mathrm{~m}$.

Finally, we determine the perimeter of the garden by starting at $P$ and proceeding clockwise. The perimeter is $9+9+1+2+8+11=40 \mathrm{~m}$.

ANSWER: (C)