Question

Using proportions to solve for missing sides.
BCD~GEF, find BD.

Answer 1

BD = 19

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