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 $$AC$$.

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, $$AC = AE + EC$$  $$AC = 4.5 + 8 = 12.5 \ cm$$ MathematicsRS AgarwalStandard X

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