Segment JI is a midsegment (given). So that means point J is a midpoint of segment HF. The midpoint cuts HF into two equal pieces. Those two pieces are HJ and JF. Therefore, HJ = JF
Using substitution, we can plug in the given expressions that the diagram shows. Then we can solve for x
HJ = JF
2x-3 = x+2
2x-3+3 = x+2+3
2x = x+5
2x-x = x+5-x
x = 5
Now that we know x = 5, use this to find the length of HG
HG = 11*x + 5
HG = 11*5 + 5
HG = 55 + 5
HG = 60
So HG is 60 inches long, which is the final answer
Note: 60 inches = 5 ft
