Flower bed tiles

A gardener lays tiles around a square flower bed. It needs 12 tiles around the 2x2 bed. How many tiles will he need around the size of the bed?

a) 9x9
b) nxn?

How big was the bed for which the gardener consumed
c) 112
d) 4n tiles?

Final Answer:

a =  40
b = 4n+4
c =  27
d =  0

Step-by-step explanation:

$$\begin{gathered} s_1=4\cdot 4-2\cdot 2=12 \\ a=(9+2)\cdot (9+2)-9\cdot 9=40 \end{gathered}$$

$$\begin{gathered} b=(n+2)\cdot (n+2)-n\cdot n \\ b=n^2-4n+4-n^2 \\ b=4n+4 \end{gathered}$$

$$\begin{gathered} 112=4\cdot c+4 \\ 4c=108 \\ c=\frac{108}{4}=27 \\ c=27 \end{gathered}$$

$$\begin{gathered} 4n=4n+4 \\ 0=4 \\ d=0 \end{gathered}$$

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