Question

In figure, ∠A = ∠CED, prove that ∆CAB ~ ∆CED. Also, find the value of x.

Answer 1

In ∆CAB and ∆CED, we have

∠A = ∠CED and ∠C = ∠C [common]

∆CAB ~ ∆CED

${\displaystyle \Rightarrow \frac{CA}{CE}=\frac{AB}{DE}=\frac{CB}{CD}}$

${\displaystyle \Rightarrow \frac{AB}{DE}=\frac{CB}{CD}\Rightarrow \frac{9}{x}=\frac{10+2}{8}}$

⇒ x = 6 cm