Question

Ramu and his three brothers owned an agricultural land of quadrilateral shape. They fenced its boundary with a thick metallic wire. Later on, they divided the land in 4 parts by fixing a thin wire along its diagonals. Which of the two wires (thick or thin) was of larger length and why?

Answer 1

Thick wire will be of larger length.
when we divide the quadrilateral into four parts, it will be four triangle.
And we know the side property of triangle , that sum of any two sides of a triangle is always greater than the third side.
Let the quadrilateral be ABCD then the diagonal AC and BD
Then, 
AB +BC > AC
BC +CD > BD
CD+ AD >AC
AD +AB >BD 
adding all,
2( AB +BC +CD +AD) > 2(AC +BD)
( AB +BC +CD +AD) > (AC +BD)
so the sum of sides of quadrilateral is greater than the sum of it's diagonal.