$Δ A B C$ is a right-angled triangle. $B D ⊥ A C$ . If and $D C = 2 c m$ , then find the length of $B D$ .

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Solution

$Δ A D B \sim Δ B D C$

$∴ \frac{A D}{B D} = \frac{B D}{D C}$

$∴ B D^{2} = A D \times D C = 8 \times 2$

$∴ B D^{2} = 16$

$∴ B D = 4 c m$

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