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Question

$$D$$ and $$E$$ are points on the sides $$AB$$ and $$AC$$ respectively of a $$\Delta ABC$$ such that $$DE || BC$$.  If $$AD = 3.6 cm, AB = 10 cm$$ and $$AE = 4.5 cm$$, find $$EC$$ and $$AC$$. 
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Solution

From given  triangle, points $$D$$ and $$E$$ are on the sides $$AB$$ and $$AC$$ respectively such that $$DE || BC$$.  
$$AD = 3.6  \ cm, \ AB = 10  \ cm$$ and $$AE = 4.5  \ cm$$. 
 
By Basic Proportonality Theorem: 
 
$$\dfrac{AD}{DB} = \dfrac{AE}{EC} $$
 
Here $$DB = AB - AD = 10 - 3.6 = 6.4 \ cm$$ 

 $$\Rightarrow EC = \dfrac{4.5}{3.6}\times 6.4$$ 
 
or $$EC = 8 \ cm$$ 
 
And, $$AC = AE + EC$$ 
 
$$AC = 4.5 + 8 = 12.5 \ cm$$ 

Mathematics
RS Agarwal
Standard X

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