Answer:
Length of segment HG=60 inches.
Length of JI=30 inches.
Step-by-step explanation:
Given , if a line JI is a midsegment of triangle FGH.
Triangle midsegment theorem: It states that when a segment formed by joining of midpoints of any two sides of a triangle then it is parallel to III side of triangle and half of its length.
JI is the midsegment , J is the midpoint of side HF and I is the midpoint of GF
Therefore, we have
HJ=JF and GI=IF
2x-3=x+2
By subtracting property of equality
2x-x=2+3
x=5 ( by simplification)
Length of side HG= 11x+5
Length of side HG=[tex]11\times 5+5=60[/tex] inches.
By substituting the value of x
JI=[tex]\frac{1}{2} HG[/tex]
By using theorem
JI=[tex]\frac{1}{2} \times60=30[/tex]
JI=30 inches.
