CBSE Class 9 Answered

A room is half as long as it is broad. The cost of carpeting the room at Rs 3.25 m2 is Rs 175.50 and the cost of preparing the walls at Rs 1.40 per m2 is Rs 240.80. If 1 door and 2 windows occupy 8 m2, then find the dimensions of the room ?

Asked by nisha_vini29 | 16 Feb, 2016, 08:46: PM

Expert Answer

begin mathsize 14px style L e t space t h e space b r e a d t h space o f space t h e space r o o m space b e space a space m. rightwards double arrow L e n g t h space o f space t h e space r o o m equals a plus a over 2 equals fraction numerator 3 a over denominator 2 end fraction m A r e a space o f space t h e space r o o m equals a cross times fraction numerator 3 a over denominator 2 end fraction equals fraction numerator 3 a squared over denominator 2 end fraction m squared rightwards double arrow C o s t space o f space c a r p e t i n g space t h e space r o o m space a t space R s. space 3.25 divided by m squared equals R s. space open parentheses 3.25 cross times fraction numerator 3 a squared over denominator 2 end fraction close parentheses rightwards double arrow 175.50 equals 3.25 cross times fraction numerator 3 a squared over denominator 2 end fraction rightwards double arrow a squared equals fraction numerator 175.50 cross times 2 over denominator 3.25 cross times 3 end fraction equals 36 rightwards double arrow a equals 6 rightwards double arrow b r e a d t h equals a equals 6 space m space a n d space l e n g t h equals fraction numerator 3 cross times 6 over denominator 2 end fraction equals 9 space m L e t space t h e space h e i g h t space o f space t h e space r o o m space b e space h space m. A r e a space o f space 4 space w a l l s equals 2 left parenthesis l plus b right parenthesis cross times h equals 2 left parenthesis 6 plus 9 right parenthesis cross times h equals 30 h space m squared A r e a space o f space 1 space d o o r space a n d space 2 space w i n d o w s equals 8 space m squared A r e a space t o space b e space p a p e r e d equals A r e a space o f space 4 space w a l l s minus space A R e a space o f space 1 space d o o r space a n d space 2 space w i n d o w s equals left parenthesis 30 h minus 8 right parenthesis m squared rightwards double arrow C o s t space o f space p a p e r i n g space w a l l s space a t space R s. space 1.40 divided by m squared equals R s. space left parenthesis 30 h minus 8 right parenthesis cross times 1.40 rightwards double arrow 240.80 equals left parenthesis 30 h minus 8 right parenthesis cross times 1.40 rightwards double arrow 30 h minus 8 equals fraction numerator 240.80 over denominator 1.40 end fraction rightwards double arrow 30 h minus 8 equals 172 rightwards double arrow 30 h equals 180 rightwards double arrow h equals 6 space m H e n c e comma space d i m e n s i o n s space o f space t h e space r o o m space a r e colon L e n g t h equals 9 space m comma space b r e a d t h space equals 6 space m space a n d space h e i g h t equals 6 space m end style

Answered by Rashmi Khot | 17 Feb, 2016, 11:17: AM

CBSE Class 9 Answered

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CBSE Class 9 Answered

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