Question

In the figure, if ACB = CDA, AC = 6 cm and AD = 3 cm, then find the length of AB
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Answer 1

Answer:

Step-by-step explanation:

given : ∠ ACB = ∠ CDA

in Δ ACB and Δ ADC

∠ ACB = ∠ ADC (given)

∠ CAB = ∠ DAC (common)

∴ Δ ACB ≅  Δ ADC ( AA similarity )

we know that

side of similar triangle are in same proportion

∴ $\frac{AC}{AD} = \frac{AB}{AC}$

putting values

$\frac{6}{3} = \frac{AB}{6}$

$2=\frac{AB}{6}$

2 × 6 = AB

AB = 12

So, length of AB is 12 cm