Inscribed rectangle

The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.

Correct answer:

S =  79.06

Step-by-step explanation:

$$\begin{gathered} a=5 \\ {S}_1=\pi r^2 \\ {r}^2=S_1\mathrm{/}\pi =216\mathrm{/}\pi =68.755 \\ {r}^2=a^2\mathrm{/}4+b^2\mathrm{/}4 \\ 4r^2=a^2+b^2 \\ {b}^2=4r^2-a^2=4\cdot 68.755-5^2 \\ b=15.812 \\ S=ab=5\cdot 15.812=79.06 \end{gathered}$$

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