Question
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC:
If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
If AD = 3.6cm, AB = 10cm and AE = 4.5cm, find EC and AC.
✓
Answer
In $\triangle\text{ABC},$ it is given that DE || BC.
Applying Thales' theorem, we get:
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\therefore\text{AD}=3.6,\text{AB}=10\text{cm},\text{AE}=4.5\text{cm}$
$\therefore\text{DB}=10-3.6=6.4\text{cm}$
or, $\frac{3.6}{6.4}=\frac{4.5}{\text{EC}}$
or, $\text{EC}=\frac{6.4\times4.5}{3.6}$
or, $\text{EC}=8\text{cm}$
Thus, $\text{AC}=\text{AE}+\text{EC}$
$=4.5 +8=12.5\text{cm}$
Applying Thales' theorem, we get:
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\therefore\text{AD}=3.6,\text{AB}=10\text{cm},\text{AE}=4.5\text{cm}$
$\therefore\text{DB}=10-3.6=6.4\text{cm}$
or, $\frac{3.6}{6.4}=\frac{4.5}{\text{EC}}$
or, $\text{EC}=\frac{6.4\times4.5}{3.6}$
or, $\text{EC}=8\text{cm}$
Thus, $\text{AC}=\text{AE}+\text{EC}$
$=4.5 +8=12.5\text{cm}$
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