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ABCD is a quadrilateral then Is AB+BC+CD+DA greater than 2(AC+BD) |
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Answer» ABCD is a quadrilateral. JOINING A to C and B to D, we get triangles, ABC, BDC, ACD and ABD. AC and BD are the diagonals.Sum of the two SIDES of a triangle is greater than the third side.So, considering the triangle ABC, BCD, CAD and BAD, we getAB + BC > ACCD + AD > ACAB + AD > BDBC + CD > BDAdding all the above equations,2(AB + BC + CA + AD) > 2(AC + BD)⇒ 2(AB + BC + CA + AD) > 2(AC + BD)⇒ (AB + BC + CA + AD) > (AC + BD)⇒ (AC + BD) < (AB + BC + CA + AD)Please mark as brainlist and FOLLOW me please |
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