$∠$ ABC and $∠$ BDC are two right angles. If AD $= 9$ cm, DC $= 16$ cm and AB $= 15$ cm, then the length of BD is __________.

12

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16

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15

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25

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Solution

The correct option is A $12$ cm
$∠ B D A = ∠ B D C = 90^{o}$
$∴ △ A B D$ is a rightangled triangle.
Thus, $A B^{2} = B D^{2} + A D^{2}$
$\Rightarrow 15^{2} = B D^{2} + 9^{2} \Rightarrow B D^{2} = 225 - 81 = 144 \Rightarrow B D = \sqrt{144} = 12 c m$

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