7. 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 papering the walls
at Rs 1.40/m² is Rs 240.80. If one
door and two windows occupy 8
m”, find the height of the room.
Answers
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