A room is 1.5 times as long as it is broad. The cost of carpeting the room at Rs 18 per sq. m is Rs 972 and the cost of white washing the four walls at the rate of Rs 6 per sq. m is Rs 1080. Find the dimensions of the room.
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Step-by-step explanation:
Let the breadth of the room be am
⇒ Length of the room=a+
2
a
=
2
3a
m
Area of the rooma×
2
3a
=
2
3a
2
sq.m
⇒ Cost of carpeting the room at Rs.3.25per sq.m=Rs.3.25×
2
3a
2
⇒75.50=3.25×
2
3a
2
⇒a
2
=
3.25×3
175.50×2
=36
⇒a=6
⇒ Breadth=a=6m and length=
2
3×6
=9m
Let the height of the room be hm
Area of 4 walls=2(l+b)×h=2(6+9)×h=30hsq.m
Area of 1 door and 2 windows=8sq.m
Area to be papered=Area of 4 walls−Area of 1 door and 2 windows
=(30h−8)sq.m
⇒Cost of papering walls at Rs.1.40per sq.m=Rs.(30h−8)×1.40
⇒240.80=(30h−8)×1.40
⇒30h−8=
1.40
240.80
=172
⇒30h=172+8=180
⇒h=
30
180
=6m
Hence, dimensions of the room are
Length=9m, Breadth=6m and Height=6m
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