Question

Question for Genius.....

Q...:- prove that 3 times of the square of any side of an equilateral triangle is equal to 4 times the square of its altitude.

pls do in paper nd clicl the pic and attach with ur answer....

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Answer 1

let ABC be the equilateral triangle .
let AD be the perpendicular bisector from A on to AC .so BD =CD=1/2 BC .
ADC is a right angled triangle AC^2=AD^2 +CD^2
AC^2=AD^2 +( 1/2AC)^2
AD^2= 3/4AC^2
4AD^2=3AC^2.
hope this answer would help u .
pls mark it as brainliest

Answer 2

Step-by-step explanation:

Given: An Equilateral triangle ABC, AE ⊥ BC.

Proof: Since ABC is an equilateral and AE is altitude,

∴ E is the mid-point of BC.

[∵ Altitude of an equilateral triangle bisects the opposite side]

Let the side of an Equilateral triangle be 'a'.

Since, ΔAEB is right-angled at E,

⇒ AB² = AE² + BE²

⇒ a² = AE² + (a/2)²

⇒ a² - a²/4 = AE²

⇒ 3a²/4 = AE²

⇒ 3a² = 4AE²

⇒ 3 * (Square of one side) = 4 * (Square of its altitude).

Hope it helps!