9514 1404 393
Answer:
(c) BK = 65
Explanation:
Corresponding sides are proportional in similar triangles, so ...
ZT/ZQ = KF/KB
27/(2x +7) = 45/(4x+1)
27(4x+1) = 45(2x +7) . . . cross-multiply
3(4x +1) = 5(2x +7) . . . . divide by 9
12x +3 = 10x +35 . . . . . eliminate parentheses
2x = 32 . . . . . . . . . . . . . subtract 10x+3
x = 16 . . . . . divide by 2
Then the length of BK is ...
BK = 4x+1 = 4·16 +1
BK = 65