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 $$AE$$.

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 $$AE = 4 \ cm$$MathematicsRS AgarwalStandard X

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