ramu and his three brothers owned an agricultural land of quadrilateral shape. They faced 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 longer length and why ?
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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.
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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