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?  

Asked by Jerlin George | 1st Apr, 2015, 05:24: PM

Expert Answer:

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.

Answered by Vimala Ramamurthy | 3rd Apr, 2015, 12:15: PM

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