Find the missing length.

Question

AP PC BQ BC

6    4    ?    13

You have two similar triangles ABC and on top inside the first triangle PQC. PQ are parallel to AB. The lengths are given. Find the missing length.

Answer 1

BQ + QC = 13

QC = 13 - BQ

 

BQ : QC :: 6 : 4

BQ : (13 - BQ) :: 6 : 4

4BQ = 6(13 - BQ)

4BQ = 78 - 6BQ

10BQ = 78

BQ = 7.8