Math, asked by kishoreranjandeepak, 4 months ago

5. In a quadrilateral OPQR, show that :
(i) sum of its sides > sum of its diagonals, and
(ii) sum of its sides < 2 (sum of its diagonals)​

Answers

Answered by s1270nandita3531
6

Answer:

2(AB+BC+CD+AD)>2(AC+BD)

AB+BC+CD+DA>AC+BD

Step-by-step explanation:

Consider a quadrilateral ABCD

Consider ΔACD

By triangle inequality

AC<AD+CD⋯(1)

Consider ΔACB

By triangle inequality

AC<AB+CB⋯(2)

Consider ΔBCD

By triangle inequality

BD<BC+CD⋯(3)

Consider ΔADB

By triangle inequality

BD<AD+AB⋯(4)

Adding all the equations

2(AB+BC+CD+AD)>2(AC+BD)

AB+BC+CD+DA>AC+BD

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