Question 1210520
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A regular hexagon has a perimeter of p (in length units) and an area of A (in square units). 
If A=3/2 then find the side length of the hexagon.
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As  I read this post  by @CPhill,  it saddens me to see how clumsily the problem is formulated 
and how poorly the solution is presented.


The part  " hexagon has a perimeter of p "  is totally irrelevant to the problem and should be omitted.


The normal formulation to this problem is as follow


<pre>
    A regular hexagon has the area of 3/2 square units. 
    Find the side length of the hexagon.
</pre>


Below is a normal mathematical solution in a form as it should be.


<pre>
Let 'a' be the side length of the regular hexagon.


This hexagon is the union of 6 equilateral triangles with the side length of 'a'.


So, the area of each such a triangle is  {{{(1/6)*(3/2)}}} = {{{1/4}}} of the square unit.


The area of each such a triangle is  {{{a^2*(sqrt(3)/4)}}}.


So, for 'a' we have this equation

    {{{a^2*(sqrt(3)/4)}}} = {{{1/4}}},

which implies

    {{{a^2}}} = {{{1/sqrt(3)}}},

    a = {{{1/root(4,3)}}} = 3^(-1/4) = 0.7598  (rounded).

<U>ANSWER</U>.  The side of the regular hexagon is  a = {{{1/root(4,3)}}} = 3^(-1/4) = 0.7598  (rounded).

<U>CHECK</U>.  {{{6*0.7598^2*(sqrt(3)/4)}}} = 1.49986  for the full area, which is a good approximation.
</pre>

Solved.


Compare this solution with the mess of words in the post by @CPhill.