Question

The altitude of an equilateral triangle is 12 centimeters. What is the perimeter of the triangle?

Answer 1

41.6cm to 1dp

Explanation:

Let's sketch the situation.

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) = 12/x`

`x = 12/tan(60) = 6.928`

`"Side Length" = 2x = 13.856`

`"Perimeter" = 3*"Side Length" = 41.568`

`color(blue)("Using Sine instead")`

`sin(60) = 12/"Side Length"`

`"Side Length" = 12/sin(60) = 13.856` and so on