​In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If the diagonal BD = x, then which one of the following is correct?​

Correct option is B

Concept Used:

The sum of the length of the two sides of a triangle is greater than the length of the third side

and the difference between the two sides of a triangle is less than the length of the third side.

Solution:

In ΔABD,

=> AD + AB > x

=> 10 + 6 > x

=> 16 > x

Also,

=> AD - AB < x

=> 10 - 6 < x

=> 4 < x

=> 4 < x < 16 ..... (i)

In ΔDBC,

=> BC + DC > x

=> 18 + 6 > x

=> 24 > x

Also,

=> BC - DC > x

=> 18 - 6 > x

=> 12 > x

=> 12 < x < 24 ...... (ii)

Combining both (i) and (ii),

12 < x < 16

∴ The correct answer is12 < x < 16.