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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 $$\dfrac{AD}{AB} = \dfrac{8}{15}$$ and $$EC = 3.5 cm$$, find $$AE$$.  

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Solution

Given : $$\dfrac{AD}{AB} = \dfrac{8}{15}$$ and $$EC = 3.5 \ cm$$

Find $$AE$$

By BPT: 
 
$$\dfrac{AD}{AB} = \dfrac{AE}{AC}$$ 
 
$$\dfrac{8}{15} = \dfrac{AE}{(AE+EC)} = \dfrac{AE}{(AE+3.5)}$$ 
 
$$8(AE + 3.5) = 15AE$$ 
 
$$7 AE = 28$$ 
 
or $$AE = 4 \ cm$$

Mathematics
RS Agarwal
Standard X

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