# Let S be a square of unit area. Consider any quadrilateral which has one vertex on each side of S. If #a,b,c and d# denote the lengths of sides of the quadrilateral, prove that #2<=a^2+b^2+c^2+d^2<=4#?

##### 1 Answer

Jul 15, 2018

Let

So

Let

Applying Pythagoras thorem we can write

Now by the problem we have

Hence