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In a ABC, D...

Question

In a $△ A B C, D$ and $E$ are points on $A B$ and $A C$ respectively such that $D E ∥ B C$ . If $A D = 24 c m$ , $A E = 3.5 c m$ , $D E = 2 c m$ and $B C = 5 c m$ , find $B D$ and $C E$ .

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Solution

$\begin{matrix} \Rightarrow \frac{A D}{A B} = \frac{A E}{A C} = \frac{D E}{B C} \Rightarrow \frac{24}{A B} = \frac{2}{5} A B = 60 c m A n d \frac{3.5}{A C} = \frac{2}{5} A C = \frac{3.5 \times 5}{2} = 8.75 c m T h e n B D = (A B - A D) = (6. - 24) = 36 c m a n d E C = (A C - A E) = (8.75 - 3.5) = 5.2 c m \end{matrix}$

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