Q24 of 35 Page 311

Jaya drew an incircle of a square. That circle is also circumscribe an equilateral triangle of which each length of side of 4√3 cm. Let us write by calculating the length of diagonal of square.


Given: Length of side of equilateral triangle = 4√3 cm


Height of equilateral triangle



The centroid of equilateral triangle is at A and lies on height BK.



⇒ BA = 4 cm


So, the radius of the circum circle of this triangle = 4 cm.


Now, diameter of the circle = 2× radius = 8 cm


⇒ IJ = 8 cm


From the figure, IJ = EH = side of the square


⇒ Side of the square = 8 cm


We know that the diagonal of a square =√2× side


⇒ FH = 8√2 cm


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