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Prove that the equilateral triangles described on the two sides of a right-angled triangle are together equal to the equilateral triangle described on the hypotenuse in terms of their areas.


Let ABC be the right triangle with perpendicular sides a and b and hypotenuse c and ADB, AEC, AFC be the equilateral triangle drawn a, b and c.

Then c2 = a2 + b2



Area of triangle AFC = Area of triangle ADB + Area of triangle BEC.


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