Question

In an equilateral triangle of height is √3 find its length of the side and perimeter

Answer 1

Hello Mate!

H^2 = B^2 + P^2
a^2 = ( a/2 ) ^ 2 + P^2
a^2 - ( a/2 ) ^2 = P^2
( a + a/2)( a - a/2 ) = P^2
3a/2 × a/2 = P^2
3a^2 / 4 = P^2
_/( 3a^2/4 ) = P
(_/3)a/2 = height

As we know that height of equilateral triangle = root 3a / 2

$\sqrt{3} = \frac{ \sqrt{3} a}{2} \\ 2unit = a \\ \\ perimeter = 3a \\ 3 \times 2 \: unit = 6 \: units$