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Ramu and his three brothers owned an agricultural land of quadrilateral shape. they fenced its boundary with a thik metallic wire. later on they divided

the land in 4 part by fixing a thin wire along its diagonals. which of the two wires ( thick or thin ) Was of larger 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.