Question 1149195
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Connect the points A and D by segment AD and consider triangles ABD and ADC.


Let "a" be the length of the side (of any of the three congruent sides) of the equilateral triangle ABC.



Then the area of the triangle ABD is  {{{(1/2)*a*8}}},

and  the area of the triangle ADC is  {{{(1/2)*a*25}}}.



The area of the whole triangle ABC is the sum of areas of triangles ABD and ADC


    {{{(1/2)*8a}}} + {{{(1/2)*25a}}} = {{{(1/2)*a*abs(AG)}}}.


Cancel the factors  {{{1/2}}}  and  "a"  in all three terms, and you will get


    | AG | = 8 + 25 = 33 cm.      <U>ANSWER</U>
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Solved.


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<U>CONCLUSION &nbsp;and &nbsp;the &nbsp;fact &nbsp;to &nbsp;MEMORIZE</U>.  


<pre>
    In any equilateral triangle, the sum of lengths of two perpendiculars from the point in one side 
    to two other sides is equal to the altitude length of the triangle.
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