Let ABC be an equilateral triangle and AD perpendicular

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Let ABC be an equilateral triangle and AD perpendicular to BC. Then AB² + BC² + CA² = ?

1. 2AD²
2. 3AD²
3. 4AD²
4. 5AD²

Correct Option: D

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

Here , AD ⊥ BC
∴ BD = DC = AB/2 = AC/2 = CB/2
Use the Pythagoras formula to get the length of AD.

AD =	√3	AB =	√3	BC =	√3	AC
	2		2		2

⇒ AB =	2	AD = BC = AC
	√3

∴ AB² + BC² + AC² =		4	+	4	+	4		AD² = 4AD²
		3		3		3