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ABCD is a given quadrilateral with AC as one of its diagonals. Then find the relation between $A B + B C + C D$ and DA.

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AB+BC+CD >DA

AB+BC+CD >2DA

AB+ BC+CD < DA

AB+BC+CD =DA

answer is A.

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Detailed Solution

Given is a quadrilateral with AC as one of its diagonals.
Question Image

We know that the sum of any two sides of the triangle is greater than the third side.
In

Δ A B C

A B + B C > A C

…… (i)
Adding CD on both the sides of (i), we get,

A B + B C + C D > A C + C D

…(ii) In

Δ A C D

A C + C D > D A

. …(iii) From the equations (ii) and (iii) we get,

A B + B C + C D > D A

.
So, the relation between

A B + B C + C D

and DA is

A B + B C + C D > D A

.
Hence, option 1 is correct.

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