Xenia K.

asked • 02/14/16

Equilateral triangle with perpendicular height h

I don't know how to go about this question :
An Equilateral triangle has perpendicular height h. A) find the length of each side, in terms of h B) without using your calculator, show that the area of the triangle is h^2/√3
 
Do I use Pythagoras? But that would be if the sides are length l : l2=(1/2l)2+h2. I don't see a way to do that in terms of h... 

1 Expert Answer

By:

Steven B. answered • 02/14/16

I love math, and love to teach it

Xenia K.

Hello, thanks for the quick answer, but my question is how do I solve x2=(1/2 x)2+h2
My solution seems to have a mistake:
x2=(1/2 x)2+h2 _I take away (1/2 x)2 and solve it to 1/4 x2
So, x2- 1/4 x2= h_solving this 
To 3/4x2=h_I divide the right side by 3/4
So, x2=4/3 h_putting a root over this 
x=(√4)/(√3) h
x=2/√3 h
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02/14/16

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