I am clueless about how to solve this. Your help is appreciated. Thanks
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