THe midpoint Theorem states:
The lines joining the midpoint of any two sides of a triangle is parallel to the third side and is half of it
In the given triangle The length of line joining the midpoints is 39 .This will be half of the third side that is [tex] n^{2} -3 [/tex]
We can form an equation:
[tex] \frac{1}{2}(n^{2} -3)= 39 [/tex]
Multiplying both sides by 2
[tex] n^{2} -3=39(2)
n^{2} -3=78 [/tex]
Adding 3 both sides
[tex] n^{2} =81 [/tex]
Taking root of both sides:
n=9
Option D is right
