MCQ
In $\triangle\text{ABC},$ D and E are points on side AB and AC respectively such that DE || BC and AD : DB = 3 : 1. If EA = 3.3cm, then AC =
- A1.1cm.
- B4cm.
- ✓4.4cm.
- D5.5cm.
✓
Answer
Correct option: C.
4.4cm.
Given: In $\triangle\text{ABC},$ D and E are points on the side AB and AC respectively such that DE || BC and AD : DB = 3 : 1. Also, EA = 3.3cm.
To find: AC
In $\triangle\text{ABC},$ DE || BC.
Using corollory of basic proportionality theorem, we have,
$\frac{\text{AD}}{\text{AB}}=\frac{\text{EA}}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\text{BD}}=\frac{3.3}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\frac{1}{3}\text{AD}}=\frac{3.3}{\text{AC}}$
$\text{EC}=4.4\text{cm}$
Hence the correct answer is C.
To find: AC
In $\triangle\text{ABC},$ DE || BC.
Using corollory of basic proportionality theorem, we have,
$\frac{\text{AD}}{\text{AB}}=\frac{\text{EA}}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\text{BD}}=\frac{3.3}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\frac{1}{3}\text{AD}}=\frac{3.3}{\text{AC}}$
$\text{EC}=4.4\text{cm}$
Hence the correct answer is C.
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