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Question

The ratio of the area of a square inscribed in a semicircle to that of the area of a square inscribed in the circle of the same radius is

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Solution

Let r be radius of semi circle.
h be side of square. (Ref. image 1)
(h2)2+h2=r2
h24+h2=r25h24=r2
h2=4r25 ……(1)
from (1) r=5h2
Same radius (Ref. image 2)
(2r)2=x2+x2
4r2=2x2
Area of square x2=2r2……..(2)
Ratio =(1)(2) =4r252r225.

1055405_1049694_ans_c4f6dfc00cd3451282ba640dd4a37061.png

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