Answer:
Explanation:
You want the missing length EG and the corresponding value of x in isosceles triangle DEF with midline GH of length 6 parallel to base DF of length 12.
Midline
The length of segment GH is half the length of segment DF (6/12 = 1/2), so we know that corresponding sides EG and ED have the same ratio:
EG/ED = 1/2
2EG = ED . . . . . . . . . . . . multiply by 2·ED
2(x -5) = (x-5)+9 . . . . . . substitute given values
2x -10 = x +4 . . . . . . . . simplify
x = 14 . . . . . . . . . . . . . add 10-x
Then the length of EG is ...
EG = 14 -5 = 9