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
[tex]2n-1=14[/tex]
solve for n
[tex]2n=14+1[/tex]
[tex]2n=15[/tex]
[tex]n=7.5\ cm[/tex]
step 2
Find the length of GJ
we know that
The Midpoint Theorem 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
[tex]GJ=\frac{1}{2}DE[/tex]
we have
[tex]GE=2n+1=2(7.5)+1=16\ cm[/tex]
substitute
[tex]GJ=\frac{1}{2}16=8\ cm[/tex]
step 3
Find the length of HK
we have that
[tex]HK=\frac{1}{2}GJ[/tex] ----> by the midpoint theorem
we have
[tex]GJ=8\ cm[/tex]
substitute
[tex]HK=\frac{1}{2}8=4\ cm[/tex]
