The perimetre of a rectangle is 240 cm. If its length is decreased by 10% and its breadth is increased by 20% , we get the same perimetre. FIND ITS Length and Breadth.

Asked by Shobhit | 8th Sep, 2015, 09:22: PM

Expert Answer:

G i v e n space t h a t space t h e space p e r i m e t r e space o f space a space r e c tan g l e space i s space 240 space c m. L e t space l space b e space t h e space l e n g t h space a n d space b space b e space t h e space b r e a d t h space o f space t h e space r e c tan g l e. T h e n comma space 2 open parentheses l plus b close parentheses equals 240 rightwards double arrow l plus b equals 240 over 2 rightwards double arrow l plus b equals 120... left parenthesis 1 right parenthesis L e t space L space b e space t h e space d e c r e a s e d space l e n g t h space a n d space B space b e space t h e space i n c r e a s e d space b r e a d t h. G i v e n space t h a t space L e n g t h space i s space d e c r e a s e d space b y space 10 percent sign T h u s comma space d e c r e a s e space i n space l e n g t h equals 10 over 100 cross times l equals l over 10 T h e r e f o r e comma space L equals l minus l over 10 equals fraction numerator 10 l minus l over denominator 10 end fraction equals fraction numerator 9 l over denominator 10 end fraction G i v e n space t h a t space B r e a d t h space i s space i n c r e a s e d space b y space 20 percent sign T h u s comma space i n c r e a s e space i n space l e n g t h equals 20 over 100 cross times b equals b over 5 T h e r e f o r e comma space B equals b plus b over 5 equals fraction numerator 5 b plus b over denominator 5 end fraction equals fraction numerator 6 b over denominator 5 end fraction T h e space p e r i m e t r e space o f space t h e space n e w space r e c tan g l e space i s equals 2 open parentheses fraction numerator 9 l over denominator 10 end fraction plus fraction numerator 6 b over denominator 5 end fraction close parentheses G i v e n space t h a t space t h e space p e r i m e t r e space o f space t h e space n e w space r e c tan g l e equals 120 equals 2 open parentheses fraction numerator 9 l over denominator 10 end fraction plus fraction numerator 6 b over denominator 5 end fraction close parentheses equals 240 rightwards double arrow fraction numerator 9 l over denominator 10 end fraction plus fraction numerator 6 b over denominator 5 end fraction equals 120 rightwards double arrow fraction numerator 9 l over denominator 10 end fraction plus fraction numerator 12 b over denominator 10 end fraction equals 120 rightwards double arrow fraction numerator 9 l plus 12 b over denominator 10 end fraction equals 120 rightwards double arrow 9 l plus 12 b equals 1200... left parenthesis 2 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 1 right parenthesis space b y 9 space a n d space s u b t r a c t i n g space f r o m space left parenthesis 2 right parenthesis comma space w e space h a v e comma 3 b equals 120 rightwards double arrow b equals 40 space c m rightwards double arrow l equals 120 minus 40 equals 80 T h u s comma 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 r e c tan g l e space a r e space 80 space c m space a n d space 40 space c m.

Answered by Vimala Ramamurthy | 9th Sep, 2015, 09:02: AM