Math, asked by poornirenu1980, 3 months ago

8.In an equilateral triangle ,prove that three times the square of one side is equal to four times the square of one of its altitudes.​

Answers

Answered by MysteriousAryan
0

\displaystyle\huge\orange{\underline{\underline{Answer}}}

To prove: 3AB² = 4AE²

Proof: Let each side of one equilateral ∆ = a

BE = 1/2a -[perpendicular bisects the side in on an equilateral ∆]

In right ∆AEB, by Pythagoras theorem

(AB)²=(AE)² + (BE)²

(a)² = (AE)² + (1/2a)²

a² = AE² + (a/2)²

a²– a²/4 = AE²

3a²/4 = AE²

3a² = 4AE²

3AB² = 4AE²

Attachments:
Similar questions