Question

Prove that three times the square of any side of an equilateral triangle is equal to four times the square ofthe altitude.​

Answer 1

............Q.E.D. ..........

Answer 2

Answer:

As explained in detail below

Step-by-step explanation:

area of an equilateral triangle can be given by equation

A=$\frac{\sqrt{3} }{4}$ $s^{2}$

where s is length of any side

also the eqn of area of any triangle can be given by

A=$\frac{1}{2} *base*altitude$

equate both equation

$\frac{\sqrt{3} }{4}$ $s^{2}$=$\frac{1}{2} *base*altitude$

for equilateral triangle we can denote base by s(any of 3 side)

$\frac{\sqrt{3} }{4}$ $s^{2}$=$\frac{1}{2} *s*altitude$

simplifying further we get

$\frac{\sqrt{3} }{2}s=altitude$

squaring and rearranging on both side

3*s= 4*altitude