In ∆ABC ∠A = ∠B = 60°, AC = √13 cm.

Home » Aptitude » Plane Geometry » Question

In ∆ABC ∠A = ∠B = 60°, AC = √13 cm. The lines AD and BD intersect at D with ∠D= 90°. If DB = 2 cm, then the length of AD is

1. 3 cm
2. 3.5 cm
3. 4 cm
4. 4.7 cm

Correct Option: A

As per the given in question , we draw a figure of a triangle ABC

Here , ∠A = ∠B = ∠C = 60°
BC = AB = AC = √13 cm
BD = 2 cm
In ∆ ABD,
AB² = BD² + AD²
⇒ (√13)² = (2)² + AD²
⇒ AD² = 13 – 4 = 9
⇒ AD = √9 = 3 cm