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

Property to be used : In a triangle the sum two sides is always greater than the third side. Consider a quadrilateral ABCD . Draw diagonal AC . we will get two triangle now. AB + BC > AC AD + CD > AC ADDING : AB + BC + AD + CD > 2 AC .........(1) Draw the other diagonal BD . Ignore AC and cosnider the two traingles with common base BD . AB + AD > BD CD + BC > BD ADDING : AB + AD + CD + BC > 2 BD ........(2) NOW ADD (1) & (2) 2 ( AB + BC + CD + AD ) > 2 ( AC + BD ) => ( AB + BC + CD + AD ) > AC + BD => ( PERIMETER OF QUADRILATERAL OR SUM OF SIDES ) > SUM OF DIAGONALS Therefore Thick Metallic Wire is of Larger Length .