9514 1404 393
Answer:
- EF = DE = 44
- FG = DG = 36
- FH = DF = 31
Step-by-step explanation:
Since EH is the perpendicular bisector of DF, ∆DEF is isosceles and sides DE and EF have the same length.
DE = EF
(9x -1) = (7x +9)
2x = 10 . . . . . . . add 1-7x
x = 5 . . . . . . . . . divide by 2
__
Similarly, marked sides GD and GF are the same length, so ...
GD = GF
(10y -4) = (7y +8)
3y = 12 . . . . . . . . . . add 4-7y
y = 4 . . . . . . . . . divide by 3
__
Now, we have what we need to calculate the side lengths.
EF = 7x+9 = 7·5 +9 = 44
DE = 9x-1 = 9·4 -1 = 44
FG = 7y+8 = 7·4 +8 = 36
DG = 10y-4 = 10·4 -4 = 36
FH = 3x+4y = 3·5 +4·4 = 31
DF = FH = 31
