Question

In rhombus abcd, a straight line through c cuts extended ad at p and extended ab at q. If dp=12ab the ratio of the lengths of bq and ab is, 1:22:13:11:1

Answer 1

Answer:

2:1    ( DP = (1/2) AB)

Step-by-step explanation:

DP = 12 AB

DP/AB = 12

in rhombus  AD ║ BC  ( AP is extension of AD )

PQ is extension of CQ & AQ is extension of AB )

=> AP ║ BC ,  AQ ║ BQ , PQ ║ CQ

=> ΔAPQ  ≅  ΔBCQ

AP/BC   = AQ/BQ

=> (AD + DP) / BC   =  (AB + BQ)/BQ

in rhombus AB = BC = CD = DA

=> (AB + 12AB)/AB =  (AB + BQ)/BQ

=> 13BQ = AB + BQ

=> 12BQ = AB

=> BQ / AB  =  1/12

=> BQ : AB =  1: 12

Correct question is

DP = (1/2)AB

Using that

(AB + AB/2)/AB =  (AB + BQ)/BQ

=> 3BQ = 2AB + 2BQ

=> BQ = 2AB

=> BQ / AB  =  2

=> BQ : AB =  2: 1