Question
In $\triangle A B C, D$ and $E$ are point on side $A B$ and $A C$ resp. such that $DE \| BC$. If $A E=2 \ cm, A D=3 \ cm$ and $B D=4.5 \ cm$ then find $C E$.
✓
Answer
In $\triangle A B C$, we have $D E \mid I B C$.
By basic proportionality theorem,
$\frac{A D}{D B}=\frac{A E}{E C}$
$\frac{3}{4.5}=\frac{A E}{E C}$
$\frac{3}{4.5}=\frac{2}{E C}$
$E C=\frac{2 \times 4.5}{3}$
$E C=\frac{9}{3}$
$E C=C E=3$
$\text { Thus } C E=3 \ cm$
By basic proportionality theorem,
$\frac{A D}{D B}=\frac{A E}{E C}$
$\frac{3}{4.5}=\frac{A E}{E C}$
$\frac{3}{4.5}=\frac{2}{E C}$
$E C=\frac{2 \times 4.5}{3}$
$E C=\frac{9}{3}$
$E C=C E=3$
$\text { Thus } C E=3 \ cm$
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