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?

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Answers

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
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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
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.
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