SOLUTION: Equilateral triangle ABC has point E on altitude AD, 1/3 of the distance from D to A. If each side of the triangle is 3 cm, the sum of the perpendiculars from E to the sides of the

Question 1168084: Equilateral triangle ABC has point E on altitude AD, 1/3 of the distance from D to A. If each side of the triangle is 3 cm, the sum of the perpendiculars from E to the sides of the triangles is, in cm
A) 2 √ 3 /3
B) 3 √ 3 /3
C) 3 √ 3
D) 4 √ 3 /3
E) 2 √ 3
https://imageshack.com/i/pmUMJPTuj
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.


For any equilateral triangle with the side length "a"   


   +---------------------------------------------------------------------------+
   |   for any point inside the triangle, the sum of the distances             |
   |
   |    from the point to the sides of the triangle is a constant value        |
   |    equal to the length of the triangle altitude, i.e. .            |
   +---------------------------------------------------------------------------+



It is easy to prove considering the areas of participating triangles.


In your case, with the side length a = 3 cm,  the answer is (and should be)



    the sum of distances from the point to the sides of the triangle

            is    cm.

But this answer is not in the list of optional answers in your post.

Therefore, the posted problem is a FAKE.

My conclusion is that EITHER the person who created/composed this problem is UNPROFESSIONAL,

OR the source for this problem is untruthful, OR BOTH.

============

I am open to accept your "THANKS" for my teaching.

Please do not post your anathemas to me for pointing your errors.

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