Answer:
[tex]MN=19\ units[/tex]
Step-by-step explanation:
we know that
The Mid-segment Theorem states that the mid-segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this mid-segment is half the length of the third side
so
Applying the mid-segment theorem we have that
[tex]2x+5=\frac{1}{2}(8x-18)[/tex]
solve for x
[tex]4x+10=(8x-18)[/tex]
[tex]8x-4x=10+18[/tex]
[tex]4x=28[/tex]
[tex]x=7[/tex]
Find MN
[tex]MN=2x+5[/tex]
substitute the value of x
[tex]MN=2(7)+5=19\ units[/tex]
