Question

If the area of a pair of diagonally opposite triangles (Formed by joining the diagonals of the quadrilateral) is 12 and 27 respectively, then the minimum area of quadrilateral ABCD is ___

Answer 1

In a quadrilateral, product of area of diagonally opposite triangles is same.

So, the product of other set of opposite triangles will be 12*27

Now, we have to find minimum a and b such that a*b=12*27 and a+b is minimum.

So a = b = 18 (as 12*27 = 324)

Hence the area of the quadrilateral = 18 + 18 + 12 + 27 = 75