In the given figure, $A B C$ is a right angled triangle. Also $F G ∥ D E ∥ B C$ and $A F = G E = E B$ . If $D E = 12 c m$ , then the measure of $B C$ is

12 c m

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18 c m

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24 c m

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30 c m

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Solution

The correct option is B $18 c m$
Let AG = GE = EB = x. Given DE = 12cm.
In $Δ D A E a n d Δ C A B, ∠ A i s c o m m o n$
$∠ D E A = ∠ C B A = 90^{0}$
$∠ A D E = ∠ A C B$ [corresponding angles]
Hence $Δ D A E \sim Δ C A B b y A A$ .
$\frac{D E}{A E} = \frac{C B}{A B} \frac{12}{2 x} = \frac{C B}{3 x} ⟹ C B = 18 c m$
$C B = 18 c m$

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