$I n t h e g i v e n f i g u r e . A B a n d D E a r e p e r p e n d i c u l a r s t o B C . I f A B = 9 c m . D E = 3 c m a n d A C = 24 c m, c a l c u l a t e A D .$

8cm

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12cm

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16cm

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10cm

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Solution

The correct option is C
16cm

$I n △ A B C a n d △ D E C : (i) ∠ A B C = ∠ D E C [E a c h 90^{0}] ((i i) ∠ C i s c o m m o n) ∴ △ A B C ≅ △ D E C [B y A . A] \Rightarrow \frac{A C}{D C} = \frac{A B}{D E} i . e \frac{24 c m}{D C} = \frac{9 c m}{3 c m} R i g h t a r r o w D C = \frac{24 \times 3}{9} = 8 c m ∴ A D = A C - D C = 24 c m - 8 c m = 16 c m$

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