Question 1149752
.
<pre>

Let the side length of the equilateral triangle ABC is "a".


Then the area of the triangle is  A = {{{a^2*(sqrt(3)/4)}}}.


The length of the base GF of the rectangle  is  b = {{{a/2}}};  

its height GD is half of the triangle height     h = {{{(1/2)*a*(sqrt(3)/2)}}} = {{{a*(sqrt(3)/4)}}}.


Hence, the area of the rectangle is  B = b*h = {{{a^2*(sqrt(3)/8)}}}.


The ratio under the question  {{{B/A}}} = {{{1/2}}}.    <U>ANSWER</U>
</pre>

Solved.