Question : For a triangle ABC, D and E are two points on AB and AC such that $\mathrm{AD}=\frac{1}{6} \mathrm{AB}$, $\mathrm{AE}=\frac{1}{6} \mathrm{AC}$. If BC = 22 cm, then DE is _______. (Consider up to two decimals)
Option 1: 1.33 cm
Option 2: 1.67 cm
Option 3: 3.67 cm
Option 4: 3.33 cm
Correct Answer: 3.67 cm
Solution :
D is a point on AB such that
AD = $\frac{1}{6}$AB and E is a point on AC such that AE = $\frac{1}{6}$AC
DE is joined.
BC = 22 cm
In triangle ADE and triangle ABC,
$\frac{AD}{AB}=\frac{AE}{EC}$
In a similar triangle, the ratio of their corresponding sides is equal.
So, $\triangle ADE \sim \triangle ABC$
Now,
$\frac{AD}{DE}=\frac{AB}{BC}$
⇒ $\frac{AD}{AB}=\frac{DE}{BC}$
⇒ $\frac{1}{6}=\frac{DE}{22}$
⇒ DE =$ \frac{22}{6}$ = 3.67
Hence, the correct answer is 3.67 cm.
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