Problems from the Dark Ages

[aeh49]

Gerbert expressed the area of an equilateral triangle of side a as (a/2)(a - a/7). Show that this is equivalent to taking (3)^1/2 = 1.714.

I don't know how to complete this problem. I tried using the formula area = 1/2*base*height. area = 1/2[(a/2)(a - a/7)^2] =1. Then I tried to solve for a, but that didn't work....

 

[royhaas]

The exact area of an equilateral triangle is \(\displaystyle \sqrt{3}a^2/4\).

 

[Deleted member 4993]

Gerbert expressed the area of an equilateral triangle of side a as (a/2)(a - a/7). Show that this is equivalent to taking (3)^1/2 = 1.714.

I don't know how to complete this problem. I tried using the formula area = 1/2*base*height. area = 1/2[(a/2)(a - a/7)^2] =1. Then I tried to solve for a, but that didn't work....

show

\(\displaystyle \sqrt 3 \, \,\mbox{ is approximated by }\, \, \frac{12}{7}\)