In Δ ABC, AB = 20 cm, BC = 7 cm and CA = 15 cm. Side BC is produced to D such that Δ DAB sim Δ DCA DC is equal to:

In Δ ABC, AB = 20 cm, BC = 7 cm and CA = 15 cm. Side BC is…

In $\Delta$ ABC, AB = 20 cm, BC = 7 cm and CA = 15 cm. Side BC is produced to D such that $\Delta$ DAB $\sim$ $\Delta$ DCA DC is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 9 cm.

Let CD = x and $\Delta$ AD = y.

DAB $\sim$ $\Delta$ DCA

AD/CD = AB/AC = BD/AD.

y/x = 20/15 = (7 + x)/y

4/3 = (7 + x)/y

4y = 21 + 3x..........(1)

y/x = 20/15

3y = 4x..................(2)

On solving equation 1 and 2 we get,

x = 9 and y = 12.