# RAmu and his three brothers owned an agricultural lsnd quadrilateral shape. They fenced its bondary 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 twi wires thick or thin was of larger length and why?

2
by jack7

2016-01-24T23:18:29+05:30
See length of diagonal is always less than the side, reason is this inequality:sum of any two sides of a triangle is larger than  the sum of other two sides,apply this inequality in all the triangles that can be formed in the quadrilateral and u will see that perimeter is greater than the sum of diagonals so thick wire is of more length.Thank You
• qais
• Content Quality
2016-01-25T08:40:05+05:30

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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