I am clueless about how to solve this. Your help is appreciated. Thanks
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$\begingroup$ Hint: the three squares have sides $\,x, 5-x, 5-2x\,$, and you know one certain point lies on the circle. $\endgroup$– dxivMar 8, 2022 at 6:16
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1$\begingroup$ Too many questions begin or end with "I don't even know how to begin with this problem". While this may be true [...], it is still not a valid reason to limit your post to the statement of the problem without any mention of your own thoughts. – From Avoid "no clue" questions. $\endgroup$– Martin RMar 8, 2022 at 6:23
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$\begingroup$ Measleading figure.... $\endgroup$– dmtriMar 8, 2022 at 7:07
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2$\begingroup$ Related (duplicate?): "Finding the total area of three squares". The question provides a solution to the problem above, but asks if what happens if the arc isn't assumed to be a semicircle. $\endgroup$– BlueMar 8, 2022 at 7:46
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1 Answer
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Use coordinate geometry. Take left bottom point of green square as origin.
Side of green square: x
Side of gray square: 5-x
Side of blue square: (5-x)-x
Centre of circle: (2.5,0) Point on circle: (3x-5,x) Radius of circle: 2.5
Use distance formula: $(x-0)^2 + (3x-7.5)^2 = 2.5^2$ x = 2 (x = 2.5 discarded(?) )
Hence sides are 2, 3, 1 Area sum = 14
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$\begingroup$ Side of green square - Side of blue square $\endgroup$ Mar 8, 2022 at 8:17