Problem Solving

30:60:90 small triangle

12 root 3 : 12 : 24 root 3

What I get is the side of the big equilateral triangle is 24 root 3 + 12

side of square=12
In the bottom left, a right angled triangle is formed. with base angle 60 degree and another base angle 90 degree
thus tan 60 = 12/base side ->base side = 12/root(3) = 4*root(3)
similarly base side of bottom right = 4*root 3.
Side of triangle = 12+4*root (3)+4*root (3) = 12 + 8*root(3)
perimeter = 3*side = 36 + 24*root(3)
IMO D

I'm gonna rule this test

Thanks

So

it's 30:60:90

12/root3 : 12 : 24/root 3

4 root 3 : 12 : 8 root 3

Side of equi triangle = 4 root 3 + 12 + 4 root 3

= 8 root 3 + 12

* 3

24 root 3 + 36

30:60:90 triangle sides conform to ratio x : x.√3 : 2x
=> x.√3 = 12
=> 2x = 12/√3 . 2 = 8√3

So the length of the side of the triangle = 12 + 8√3
=> perimeter = 3(12+8√3) = 36 + 24√3

Sometimes using a/Sin A = b/Sin B = c/Sin C also helps finding sides from angles if we don't remember the 30:60:90 formula.

D is correct..

36+24root3 is the answer

Hi,
30:60:90 triangle sides are in the ratio, x: x√3:2x

so x√3=12 base of the right triangle ---> base of the equilateral triangle= 2(12/√3)+side of square i.e 12
simplifying we get value as 8√3+12.
perimeter of equilateral triangle=3*(8√3+12)---hence ans D