geometery triangle question- only one side given

[sarang]

Hi all,
If you could please help me with this triangle question.

thanks!
S

[prasantnaidu]

Hi Sarang,
The standard formula of finding the ht of a equilateral triangle is
(root 3/2) * side.
So (root 3/2)* side=4 root 3(given)
so side = 8

Thus perimeter= 8*3= 24
Hope that make you happy.
if you want some more ways of solving then you can look here
https://www.beatthegmat.com/gmat-prep-pr ... 10809.html

Keep Rocking,
Prasant.

[tohellandback]

or better remember this
property of a 30-60-90 triangle,
sides will be int he ration 1:sqrt(3):2.
side opp angle 30-1
side opp angle 60-sqrt(3)

same way, 45-45-90 triangle has sides in ratio 1:1:sqrt(2)

[Musiq]

I agree with the posters above that it is very important to know the ratios of sides of standard Right triangles 90/45/45 and 90/60/30.

A good way to know this is being tested is if you see SQRT(2 )or SQRT(3) in the answer choices. That's almost always an indicator that you will need the ratios.