Question

Pqr is an equilateral triangle of side 4a then length of its altitude is

Answer 1

Step-by-step explanation:

Formula for height of equilateral triangle=

$\sqrt{3}a \div 4$ where a= side of triangle

So,

height=root3×4a/4

=a×root3

Answer 2

answer: 2√3a²

proof:

let the side be a= 4a

let the length of altitude be b

since the altitude divides the triangle into two congruent triangles and bisects the base..

therefore the triangles formed are rightΔs

lets take one right triangle

we know that hyp²=s1²+s2²

the hyp= 4a

s1=base= 2a

s2= b= altitude

16a²=4a²+b²

b²=12a²

b=√12a²

b=2√3a²