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

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11 cm

13 cm

10 cm

12 cm

answer is D.

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Detailed Solution

Given that, ∠ACB = ∠CDA, AC = 6 cm and AD = 3 cm in the triangle ABC.
Question Image

Applying AA similarity criterion of similarity of triangles in ΔACB and ΔCDA,

∠ CAB = ∠ DAC [common angle] ∠ ACB = ∠ CDA [given] ∴ Δ A C B ~ Δ A D C [A A similarity criterion]

We know that, the ratio of the corresponding sides of the similar triangles are equal.
So,

A C A D = A B A C … … (1)

We already have, AC = 6 cm and AD = 3 cm.
Substitute above values in eq (1) and simplify.

63 = A B 6 3 A B = 6 × 6 A B = 363 A B = 12 cm

Hence, the length of AB is 12 cm.
The correct option is (4).

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