ABCD is a quadrilateral in which BD and AC are diagonals

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ABCD is a quadrilateral in which BD and AC are diagonals then

1. AB + BC + CD + AD < AC + BD
2. AB + BC + CD + DA > AC + BD
3. AB + BC + CD + DA = AC + BD
4. AB + BC + CD + DA > 2 (AC + BD)

Correct Option: B

According to question , we draw a figure of quadrilateral ABCD

We know that the sum of two sides of a triangle is greater than the third side.
∴ AB + BC > AC
BC + CD > BD
CD + AD > AC
DA + AB > BD
On adding, we get
2 (AB + BC + CD + DA) > 2 (AC + BD)
⇒AB+BC + CD + DA > (AC + BD)