In the given figure, AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm, AC = 10 cm. Find the length of AD

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Solution

Q.
In the given figure, AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm, AC = 10 cm. Find the length of AD

Ans.
(7.5)

In $∆ A B C, \frac{A P}{A B} = \frac{3}{5}$ ....(i)

$\frac{A Q}{A C} = \frac{6}{10} = \frac{3}{5}$ ...(ii)

From (i) and (ii), we get $\frac{A P}{A B} = \frac{A Q}{A C} \Rightarrow P Q ∥ B C$

In $∆ A B D, P R ∥ B D \Rightarrow \frac{A P}{A B} = \frac{A R}{A D} \Rightarrow \frac{3}{5} = \frac{4.5}{A D} \Rightarrow A D = 7.5 cm$

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