ΔABC is an equilateral triangle and AD ⊥ BC, where D lies on BC. If AD = 4√3 cm, then what is the perimeter (in cm) of ΔABC ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 24
Explanation:
AD = 4√3 cm
In right angle Δ ABD,
(∵ ∠D = 90o)
By Pythagoras theorem:
(AB)2 = (AD)2 + (BD)2
(AB = AC = BC)
(BD = BC/2 = AB/2)
⇒ (AB)2 - (BD)2 = (AD)2
⇒ (AB)2 - (AB/2)2 = (4√3)2
⇒ 3/4(AB)2 = 48
⇒ (AB)2 = 64
⇒ AB = 8 cm
Perimeter of Δ ABC = 3 × side = 3 × 8 = 24 cm