Since both rectangles are similar, the following ratio must be fulfilled:
![\frac{x+9}{14}=\frac{9}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B9%7D%7B14%7D%3D%5Cfrac%7B9%7D%7B6%7D)
By multiplying both sides by 14, we get
![\begin{gathered} x+9=\frac{9\times14}{6} \\ x+9=21 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%2B9%3D%5Cfrac%7B9%5Ctimes14%7D%7B6%7D%20%5C%5C%20x%2B9%3D21%20%5Cend%7Bgathered%7D)
and by subtracting 9 to both sides, we have
![x=12](https://tex.z-dn.net/?f=x%3D12)
Therefore, the answer is 12.
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Dimension of smaller garden :
l = 1/2 ft.
b = 2/3 ft.
Dimension of bigger garden :
L = 4 ft.
Let , breadth be x ft.
We know , area is given by :
Area = L×B.
Area of small garden = ![\dfrac{1}{2}\times\dfrac{2}{3}=\dfrac{1}{3}\ ft^2](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%5Cdfrac%7B2%7D%7B3%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5C%20ft%5E2)
Area of big garden ![=4\times x=4x\ ft^2](https://tex.z-dn.net/?f=%3D4%5Ctimes%20x%3D4x%5C%20ft%5E2)
Hence, this is the required solution.