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Basic Proportionality Theorem

In the figure...

Question

In the figure,line $P Q | | s i d e B C, A P = 2.4 c m, P B = 7.2 c m, Q C = 5.4$ cm then find $A Q$ ?

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Solution

$∵ P Q ∥ B C \Rightarrow ∠ A P Q = ∠ A B C a n d ∠ A Q P = ∠ A C B (c o r e s p o n d i n g a n g l e a r e s a m e) ∴ △ A P Q \sim △ A B C (A A c r i t e r i a) h e n c e, \frac{A P}{A B} = \frac{A Q}{A C} \Rightarrow \frac{A B}{A P} = \frac{A C}{A Q} \Rightarrow \frac{A B}{A P} - 1 = \frac{A C}{A Q} - 1 \Rightarrow \frac{P B}{A P} = \frac{Q C}{A Q} \Rightarrow \frac{7.2}{2.4} = \frac{5.4}{A Q} \Rightarrow A Q = 1.8 c m$

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