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CBSE Class 9 Answered

Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show that perimeter of the parallelogram is greater than that of rectangle.
Asked by dimplesharma0810 | 28 Feb, 2016, 08:57: PM
answered-by-expert Expert Answer
begin mathsize 14px style S i n c e space o p p o s i t e space s i d e s space o f space p a r a l l e log r a m space a n d space r e c tan g l e space a r e space e q u a l comma space w e space h a v e A B equals D C space space space space space... left parenthesis A B C D space i s space a space p a r a l l e log r a m right parenthesis A n d comma space A B equals E F space space space space space.... left parenthesis A B E F space i s space a space r e c tan g l e right parenthesis rightwards double arrow D C equals E F space space space space space space space space..... left parenthesis 1 right parenthesis rightwards double arrow A B plus D C equals A B plus E F space space space space space space.... left parenthesis 2 right parenthesis S i n c e comma space o f space a l l space t h e space s e g m e n t s space t h a t space c a n space b e space d r a w n space t o space a space g i v e n space l i n e space f r o m space a space p o i n t space n o t space l y i n g space o n space i t comma space t h e space p e r p e n d i c u l a r space s e g m e n t space i s space t h e space s h o r t e s t comma B E space less than space B C space a n d space A F less than A D rightwards double arrow B C greater than B E space a n d space A D greater than A F rightwards double arrow B C plus A D greater than B E plus A F space space space space space space space space.... left parenthesis 3 right parenthesis A d d i n g space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma A B space plus space D C plus B C plus A D greater than A B plus E F plus B E plus A F rightwards double arrow A B plus B C plus C D plus D A greater than A B plus B E plus E F plus F A i. e. comma space p e r i m e t e r space o f space a space p a r a l l e log r a m space greater than space P e r i m e t e r space o f space r e c tan g l e end style
 
Answered by Rashmi Khot | 29 Feb, 2016, 11:27: AM

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