Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?

Correct answer:

s =  4.4721 cm

Step-by-step explanation:

$$\begin{gathered} r^2=s^2+(s\mathrm{/}2{)}^2 \\ {r}^2=s^2+s^2\mathrm{/}4 \\ {r}^2=5\mathrm{/}4s^2 \\ (D\mathrm{/}2{)}^2=5\mathrm{/}4s^2 \\ s=D\mathrm{/}\sqrt{5} \\ s=10\mathrm{/}\sqrt{5}=4.4721\text{ cm} \end{gathered}$$

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