Question
Wed April 01, 2015 By: Jerlin George

The perimeter of a rectangular sheet when folded along the breadth is 28cm, whereas when it is folded along the length the perimeter is 32cm. If the folded parts are congruent in each case, then what is the original length and breadth of the paper?  

Expert Reply
Vimala Ramamurthy
Fri April 03, 2015
L e t space l space a n d space b space b e space t h e space o r i g i n a l space d i m e n s i o n s space o f space t h e space p a p e r. W h e n space f o l d e d space a l o n g space t h e space l e n g t h comma space t h e space l e n g t h space w i l l space r e m a i n space t h e space s a m e space a n d space t h e space b r e a d t h space w i l l b e space h a l f space o f space t h e space o r i g i n a l space d i m e n s i o n. T h u s comma space f r o m space t h e space g i v e n space s t a t e m e n t comma space 2 open parentheses l plus b over 2 close parentheses equals 32 space c m... left parenthesis 1 right parenthesis W h e n space f o l d e d space a l o n g space t h e space b r e a d t h comma space t h e space b r e a d t h space w i l l space r e m a i n space t h e space s a m e space a n d space t h e space l e n g t h space space w i l l b e space h a l f space o f space t h e space o r i g i n a l space d i m e n s i o n. T h u s comma space f r o m space t h e space g i v e n space s t a t e m e n t comma space 2 open parentheses l over 2 plus b close parentheses equals 28 space c m... left parenthesis 2 right parenthesis R e w r i t i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma l plus b over 2 equals 16 l over 2 plus b equals 14 T h a t space i s space w e space h a v e comma 2 l plus b equals 32... left parenthesis 3 right parenthesis a n d l plus 2 b equals 28... left parenthesis 4 right parenthesis S o l v i n g space e q u a t i o n s space left parenthesis 3 right parenthesis space a n d space left parenthesis 4 right parenthesis comma space w e space h a v e space b equals 8 space c m space a n d space l equals 12 space c m.
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