Question

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

Answer 1

Answer:

in equilateral triangle all sides are equal.

Step-by-step explanation:

ABC is a equilateral triangle. the square of all sides equal to AC equal to BC a b equal to BC and CA equal to AC

Answer 2

Answer:

Step-by-step explanation:

Let each of the equilateral triangle = a

Let the Altitude = h

To Prove 3$a^{2}$ = 4$h^{2}$

For Equilateral Triangle we know that

$\sqrt{3}$/2xa = h

Squaring at both sides , we will get

$\sqrt{3}$/2xa x  $\sqrt{3}$/2xa = h x h

3$a^{2}$/4 = $h^{2}$

ie 3$a^{2}$ = 4$h^{2}$

Therefore, three times the square of one side of an equilateral triangle is equal to four times the square of its altitude

Hence Proved