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 .