Question

In the figure, if angle ACB = angle CDA,AC = 6 cm and AD = 3 cm, then find the length of AB

Answer 1

Hi there,

The figure required for the question is missing. I have attached a figure below that satisfies the question given and have solved it accordingly.

Answer: 12 cm

Step-by-step explanation:

Given data:

∠ACB = ∠CDA

AC = 6 cm

AD = 3 cm

To find: the length of AB

Solution:

Let’s take ∆ ABC & ∆ ACD, we get

∠ACB = ∠CDA ….. [given in the question]

∠A = ∠A ….. [common angle to both the triangles]

∴ By AA similarity, ∆ ABC ~ ∆ ACD

Since the corresponding sides of the two similar triangles are proportional.

∴ AB/AC = AC/AD

On substituting the given values of AC & AD, we get

⇒ AB = AC² / AD

⇒ AB = 6² / 3 = 36/3

⇒ AB = 12 cm

Thus, the length of the side AB is 12 cm.

Hope this is helpful!!!!