Answer:
AB is 16; DG is 18
Step-by-step explanation:
Given:
- AC = 3x+2
- GC = y +1
- BC = 4x
- DC = 2y -7
- AC = BC, DC = GC
Find:
AB, DG
Solution:
Using the given expressions in the equations relating the line segments, we have ...
AC = BC
3x +2 = 4x
2 = x . . . . . . . . . subtract 3x
AC = BC = 4(2) = 8
AB = AC +BC = 8 +8 = 16
__
DC = GC
2y -7 = y +1
y = 8 . . . . . . . add 7-y
DC = GC = (8) +1 = 9
DG = DC +GC = 9 +9 = 18
Leg AB is 16; leg DG is 18.
_____
Additional comment
The geometry described in this problem statement is impossible. If the 39° angle is accurate, then the angle where the legs cross is 95.9°. If the 101° angle is accurate, then the longer leg makes an angle of about 36.7° with the table top.
