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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.