Question : In $\triangle$ABC, $\angle$A = $\angle$B = 60°, AC = $\sqrt{13}$ cm, the lines AD and BD intersect at D with $\angle$D = 90°. If DB = 2 cm, then the length of AD is:
Option 1: 3 cm
Option 2: 3.5 cm
Option 3: 4 cm
Option 4: 4.7 cm
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Correct Answer: 3 cm
Solution :
$\angle$C = 180° – 60° – 60° = 60°
So, it is an equilateral triangle.
$\therefore$ AB = BC = AC = $\sqrt{13}$ cm
In $\triangle$ADB,
AB
2
= AD
2
+ DB
2
⇒ AD = $\sqrt{(\sqrt{13})^2-2^2}=\sqrt{9}=3$ cm
Hence, the correct answer is 3 cm.
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