SOLUTION: Find the length of the segment joining the two midpoints of the sides of the triangle if the length of the third side opposite to it is 30 cm.

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Question 1082340: Find the length of the segment joining the two midpoints of the sides of the triangle if the length of the third side opposite to it is 30 cm.
Answer by ikleyn(52754) About Me  (Show Source):
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Find the length of the segment joining the two midpoints of the sides of the triangle if the length of the third side opposite to it is 30 cm.
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Notice that the formulation of this problem is NOT PERFECT.

The correct formulation is THIS: 

    Find the length of the segment joining the two midpoints of the sides of the triangle if the length of the third side is 30 cm."


I omitted the words "opposite to it" because they make it unclear "who is opposite to whom". 

Now, the answer is: 15 cm.


Solution


There is this very famous theorem of elementary geometry:


     The straight segment connecting midpoints of the two sides of a triangle is of half of the length of the third side of the triangle. 


See the lesson The line segment joining the midpoints of two sides of a triangle in this site.


So, apply this theorem, and you will get the answer in 1 second.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part if this textbook under the topic "Properties of triangles".