Question
In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If AD = 6cm, DB = 9cm and AE = 8cm, find AC.
If AD = 6cm, DB = 9cm and AE = 8cm, find AC.
✓
Answer
We have,DE || BC
therefore, by basic proportionally theorem,
We have $\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{6}{9}=\frac{8}{\text{EC}}$
$\Rightarrow\frac{2}{3}=\frac{8}{\text{EC}}$
$\Rightarrow\text{EC}=\frac{8\times3}{2}$
$\Rightarrow\text{EC}=12\text{cm}$
$\Rightarrow\text{Now, AC}=\text{AE}+\text{EC}=8+12=20\text{cm}$
$\therefore\text{AC}=20\text{cm}$
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