Step-by-step explanation:
As equilateral triangle have equal sides
By applying Pathagores theorem
[tex](hyp)^2=(per)^2+(base)^2[/tex]
by putting values
[tex](a)^2=(per)^2+( \frac{a}{2} )^2[/tex]
[tex]a^2- \frac{a^2}{4} =(per)^2[/tex]
by taking lcm on L:H:S
[tex] \frac{4a^2-a^2}{4} =(per)^2[/tex]
[tex] \frac{3a^2}{4} = (per)^2[/tex]
by taking square root on both side
[tex] \frac{ \sqrt{3}a }{2} =(per)[/tex]
i hope u will understand
