Mensurationhard · Past Paper
A square is inscribed in an equilateral triangle of side 12 cm. Find the area of the square.
A144(2*sqrt(3)-3) sq. cm
B144 / (2+sqrt(3))^2 sq. cm
C432(7-4*sqrt(3)) sq. cm
D24 sq. cm
✓ Correct Answer: C — 432(7-4*sqrt(3)) sq. cm
Let square side be x. By similar triangles, x = (12*sqrt(3))/(2+sqrt(3)). Area = x^2 = 432(7-4*sqrt(3)) after rationalizing.
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