In a trapezium ABCD, A B parallel to space C D space a n d space angle D equals 2 angle B. space I f space D C space equals space p space a n d space A D space equals space q comma space t h e n space f i n d space t h e space l e n g t h space o f space A B.

Asked by a.behera67 | 4th Jan, 2016, 09:10: PM

Expert Answer:

begin mathsize 12px style Given colon In space square ABCD space AB parallel to CD comma space angle straight D space equals 2 angle straight B comma space DC space equals space straight p space and space AD space equals straight q Let space space angle straight B space equals space straight x therefore angle straight D space equals space 2 straight x Construct space DE parallel to BC Now comma space in space square BCDE comma AB parallel to CD space... left parenthesis Given right parenthesis DE parallel to BC space space... left parenthesis By space construction right parenthesis therefore square BCDE space is space straight a space parallelogram space left parenthesis both space the space pairs space of space opposite space sides space are space parallel right parenthesis therefore DC space equals space BE space equals space straight p space left parenthesis Opposite space sides space of space parallelogram right parenthesis Also comma space angle straight B space equals space angle straight D space equals space straight x space... left parenthesis Opposite space angles space of space parallelogram right parenthesis In space triangle AED comma angle straight D space equals space 2 straight x space minus space straight x space equals space straight x space angle straight E equals angle straight D space... space left parenthesis Alternate space angles right parenthesis therefore triangle AED space is space an space iso s celes space triangle therefore AD space equals space AE space equals space straight q space... left parenthesis Sides space opposite space to space equal space angles right parenthesis AB space equals space AE space plus space BE space equals space straight q space plus space straight p therefore AB space equals space straight p space plus space straight q end style
 
 

Answered by Priti Shah | 5th Jan, 2016, 12:45: PM