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 lar ger length and why?

Answer 1

in a triangle sum of two sides is greater than the third side
consider a quad abcd   draw a diagonal ac =>ab+bc>ac and cd+da>ac
=> ab+bc+cd+da>2ac
similarly ab+bc+cd+da>2bd
=> 2(ab+bc+cd+da)>2(ac+bd)
=> ab+bc+cd+da>ac+bd
=> perimeter of quad abcd>sum of the diagonals
thick wire is of larger length