Semicircle

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

Result

s =  4.472 cm

Solution:

r2=s2+(s/2)2 r2=s2+s/4 r2=5/4s2 (D/2)2=5/4s2  s=D/5 s=10/5=4.472  cm r^2 = s^2 + (s/2)^2 \ \\ r^2 = s^2+s^/4 \ \\ r^2 = 5/4 s^2 \ \\ (D/2)^2 = 5/4 s^2 \ \\ \ \\ s = D / \sqrt{5} \ \\ s = 10 / \sqrt{5} = 4.472 \ \text { cm }

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