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 = 2.5cm, BD = 3.0cm, and AE = 3.75cm, find the length of AC.
✓
Answer
It is given that AD = 2.5cm, AE = 3.75cm and BD = 3cm.
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{CE}}$ (by thales theorem)
Then $\frac{2.5}{3}=\frac{3.75}{\text{CE}}$
$2.5\text{CE}=3.75\times3$
$\text{CE}=\frac{3.75\times3}{2.5}$
$=\frac{11.25}{2.5}$
$=4.50$
Now
$\text{AC}=3.75\text{cm}+4.50\text{cm}$
$=8.25\text{cm}$
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{CE}}$ (by thales theorem)
Then $\frac{2.5}{3}=\frac{3.75}{\text{CE}}$
$2.5\text{CE}=3.75\times3$
$\text{CE}=\frac{3.75\times3}{2.5}$
$=\frac{11.25}{2.5}$
$=4.50$
Now
$\text{AC}=3.75\text{cm}+4.50\text{cm}$
$=8.25\text{cm}$
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