Bunuel wrote:
The figure above shows the shape and dimensions of a floor that is to be carpeted. The desired carpet costs $30 per running meter, comes on a roll 6 meters wide, and has a finished surface on only one side. If AC=12 meters and if the only seam that is permitted is along the line through B and D, how much will the carpet cost?
A. $360
B. $390
C. $480
D. $540
E. $780
Attachment:
The attachment d1.JPG is no longer available
6m wide roll will cost 30$ per running meter = 1 meter length
--> to cover an area of 6*1 = 6 m^2, cost = 30 $
The figure is divided into a rectangle ACGF and an isosceles triangle DFG
E is the midpoints of base FG with FE = EG = 12/2 = 6
We know that triangle DEF is right angled
--> DF^2 = DE^2 + FE^2
--> 10^2 = DE^2 + 6^2
--> DE^2 = 100 - 64 = 36
--> DE = 6 m
The carpet will run from AC (12 meters wide) till point D
Height of roll, DB = DE + EB = 8 + 5 = 13
per running meter of roll i.e 1 meter = 30$
For 13 meter running, Cost = 13*30 = 390 $
2 rolls are required to cover (running from AB & BC) = 780 $
IMO Option E
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