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 = 4cm, DB = 4.5cm and AE = 8cm, find AC.
If AD = 4cm, DB = 4.5cm and AE = 8cm, find AC.
✓
Answer
It is given that AD = 4cm, DB = 4.5cm and AE = 8cm.
We have to find AC.
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{CE}}$ (by thales theorem)
Then $\frac{4}{4.5}=\frac{8}{\text{AC}}$
$\text{AC}=\frac{4.5\times8}{4}\text{cm}$
$=9\text{cm}$
Hence AC = 9cm.
We have to find AC.
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{CE}}$ (by thales theorem)
Then $\frac{4}{4.5}=\frac{8}{\text{AC}}$
$\text{AC}=\frac{4.5\times8}{4}\text{cm}$
$=9\text{cm}$
Hence AC = 9cm.
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