Fountain sidewalk area

A 2 m wide sidewalk is built around the circular fountain. The radii of the circles that delimit the path on both sides are 4:3. What area in square meters does this sidewalk occupy?

Final Answer:

S =  87.9646 m²

Step-by-step explanation:

$$\begin{gathered} r_1=r_2+2 \\ {r}_1=\frac{4}{3}\cdot r_2 \\ {r}_1=4/3\cdot r_2 \\ {r}_1-r_2=2 \\ 3r_1-4r_2=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 0.33r_2=2 \\ {r}_2=\frac{2}{0.33333333}=6 \\ {r}_1=\frac{0+4r_2}{3}=\frac{0+4\cdot 6}{3}=8 \\ {r}_1=8 \\ {r}_2=6 \\ S=\pi \cdot r_1^2-\pi \cdot r_2^2=3.1416\cdot 8^2-3.1416\cdot 6^2=87.9646{\text{m}}^2 \end{gathered}$$

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