Question

In an
equilateral triangle ABC, if AD is perpendicular
to BC then

(A) 2AB²=3AD²
(B) 4AB²= 3AD²
(C) 3AB²=2AD²
(D) 3AB²= 4AD²​

Answer 1

EXPLANATION.

In an equilateral triangle ABC.

AD is perpendicular (⊥) to BC.

As we know that,

Formula of Pythagoras Theorem.

⇒ H² = P² + B².

Hypotenuse > Perpendicular > Base.

Using this formula in equation, we get.

⇒ AB = BC = AC.

⇒ BC = BD + DC.

⇒ BD = 1/2BC.

We can write equation as,

⇒ (AB)² = (AD)² + (BD)².

⇒ (AB)² = (AD)² + (1/2BC)².

⇒ (AB)² = (AD)² + (1/2AB)².

⇒ (AB)² = (AD)² + (AB)²/4.

⇒ (AB)² - (AB)²/4 = (AD)².

⇒ [4(AB)² - (AB)²]/4 = (AD)².

⇒ 3(AB)²/4 = (AD)².

⇒ 3(AB)² = 4(AD)².

Option [D] is correct answer.