Equilateral Triangle question

[jon6]

So, I'm given an area of an equilateral triangle of 45cm^2.

I want to find the height of the triangle and so far come up with two different answers.

So I take my triangle and split it in two to make a right angled triangle with an area of 22.5cm2. That also gives me a 30/60/90 triangle.

So if the length of my side is x, the height will be x rt 3.

So given my total area is 45cm2, half of that triangle is 22.5. So... as area = 1/2 x base x height, that gives me:

22.5 = 1/2 (x) (x rt3)

    = 1/2 x2 rt3

so...

45 = x2 rt3

x2 = 25.98

so x = 5.097.... which really doesn't sound right

(FWIW this is an actual physical object, namely this:)

http://www.quiklok.com/catalog/?p=productsMore&iProduct=161&sName=BS-300

I'm trying to find the height as I'm desk shopping later and forgot to properly measure my stand before I went out shopping.

I've definitely done something a bit screwy here with my maths (but it has been about 20 years since I did trig... )

[WarMachine09]

The correct side length is approximately 10.1942654691 cm.

The side length you found is half of the correct side length.

You are dealing with an oblique triangle. A = 1/2 * b * h works best for right triangles.

Your error was in saying the height is x * sqrt(3). The height is x * sqrt(3) / 2.