# area of an equilateral triangle

• May 31st 2010, 09:29 AM
Mukilab
area of an equilateral triangle
the area of an equilateral triangle is 36cm^2
Each side is x

Find the value of x

I tried

bh*1/2=36

$\displaystyle \frac{1}{2}\frac{x}{1}\frac{72}{x}=36$

but that just ends up cancelling everything. What do I do?

It looks like x=1 but I'm not sure :/
• May 31st 2010, 09:39 AM
Unknown008
$\displaystyle Area\ of\ triangle = \frac12 bh$

$\displaystyle 36 = \frac12 bh$

But in an equilateral triangle, $\displaystyle \frac{b\sqrt{3}}{2} = h$ (from pythagoras' theorem)

Sub in your formula:

$\displaystyle 36 = \frac12 b(\frac{b\sqrt{3}}{2})$

You should be able to solve for the length of the base now. :)
• May 31st 2010, 09:50 AM
Mukilab
nope :/

$\displaystyle 36=\frac{72x}{2x}(\frac{x\sqrt{3}}{2})$

$\displaystyle 36=\frac{72x^2+72x\sqrt{3}}{4x}$

???
• May 31st 2010, 10:02 AM
Unknown008
Come on, it's not difficult. :)

$\displaystyle 36 = \frac12 b(\frac{b\sqrt{3}}{2})$

$\displaystyle 36 \times 2 \times 2 = b \times b \times \sqrt{3}$

$\displaystyle b^2 = \frac{144}{\sqrt{3}}$

Then take square root on both sides to get the length of the base, which is also equal to x.