Answer:
Option B) 4 centimeters
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the value of n
we know that
a) GJ is a midsegment of triangle DEF
then
G is the midpoint segment DF and J is the midpoint segment EF
DG=GF and EJ=JF
b) HK is a midsegment of triangle GFJ
then
H is the midpoint segment GF and K is the midpoint segment JF
GH=HF and JK=KF
In this problem we have
HF=7 cm
so
GH=7 cm
GF=GH+HF ----> by addition segment postulate
GF=7+7=14 cm
Remember that
DG=GF
substitute the given values
![2n-1=14](https://tex.z-dn.net/?f=2n-1%3D14)
solve for n
![2n=14+1](https://tex.z-dn.net/?f=2n%3D14%2B1)
![2n=15](https://tex.z-dn.net/?f=2n%3D15)
![n=7.5\ cm](https://tex.z-dn.net/?f=n%3D7.5%5C%20cm)
step 2
Find the length of GJ
we know that
The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
so
![GJ=\frac{1}{2}DE](https://tex.z-dn.net/?f=GJ%3D%5Cfrac%7B1%7D%7B2%7DDE)
we have
![GE=2n+1=2(7.5)+1=16\ cm](https://tex.z-dn.net/?f=GE%3D2n%2B1%3D2%287.5%29%2B1%3D16%5C%20cm)
substitute
![GJ=\frac{1}{2}16=8\ cm](https://tex.z-dn.net/?f=GJ%3D%5Cfrac%7B1%7D%7B2%7D16%3D8%5C%20cm)
step 3
Find the length of HK
we have that
----> by the midpoint theorem
we have
![GJ=8\ cm](https://tex.z-dn.net/?f=GJ%3D8%5C%20cm)
substitute
![HK=\frac{1}{2}8=4\ cm](https://tex.z-dn.net/?f=HK%3D%5Cfrac%7B1%7D%7B2%7D8%3D4%5C%20cm)