Question

what is the perimeter of an equiateral triangle whose altitude is 10 cm??

Answer 1

Every side of an equilateral triangle is the same length by definition, so once we find one side we shall have the perimeter.

Looking at the right hand side of the triangle, we see it forms a smaller, right angled triangle. We can use trigonometry to find x.
Remember SOH CAH TOA and observe that we have the opposite side and are looking for the adjacent - we use tangent. (NB: Sine would work equally well and would in fact immediately give the side length, but I already put the x in place on my wee pic).

tan(60)=12x

x=12tan(60)=6.928

Side Length=2x=13.856

Perimeter=3⋅Side Length=41.568

Using sine instead

sin(60)=12Side Length

Side Length=12sin(60)=13.856

Answer 2

By trigonometry, we can find the side length of Equilateral triangle.

Sin60° = 10/s

√3/2 = 10/s
S = 20/√3
= 20√3/3

Perimeter = 3s
= 3(20√3/3)
= 20√3 cm