Answer:
BD = 19
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so we have ...
BD/GF = BC/GE
(2x -7)/57 = (x +4)/51 . . . . use the values marked on the diagram
17(2x -7) = 19(x +4) . . . . . . . . multiply by 969
34x -119 = 19x +76 . . . . . eliminate parentheses
15x = 195 . . . . . . . . . add 119-19x
x = 13 . . . . . . . . . . divide by 15
BD = 2(13) -7 . . . . use the found value of x in the expression for BD
BD = 19
