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CAT 2004 Question Paper Question 25
Question 25

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be?

Solution

Consider side of the cube as x.

So diagonal will be of length $$\sqrt{3}$$ * x.

Now if diagonals are side of equilateral triangle we get area = 3*$$\sqrt{3}*x^2$$ /4 .

Also in a triangle

4 * Area * R = Product of sides

4* 3*$$\sqrt{3}*x^2$$ /4 * R = .3*$$\sqrt{3}*x^3$$

R = x

 


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