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805+ (Hard)|   Geometry|      
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Bunuel
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The figure above shows the shape and dimensions of a floor that is to 21 Jun 2019, 00:31
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95% (hard)

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44% (02:45) correct 56% (03:02) wrong based on 68 sessions

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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

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The figure above shows the shape and dimensions of a floor that is to 21 Jun 2019, 04:20
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Bunuel

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

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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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jfranciscocuencag
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The figure above shows the shape and dimensions of a floor that is to 21 Jun 2019, 13:38
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Dillesh4096
Bunuel

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

Show Spoiler
Attachment:
d1.JPG


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

Pls Hit Kudos if you like the solution
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Hello Dillesh4096

Why if the uper part is a iscoceles triangle we are not using 1 : 1 : root2?

Kind regards!
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The figure above shows the shape and dimensions of a floor that is to 21 Jun 2019, 13:46
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jfranciscocuencag
Dillesh4096


Hello Dillesh4096

Why if the uper part is a iscoceles triangle we are not using 1 : 1 : root2?

Kind regards!
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Hi jfranciscocuencag,

1:1:\(\sqrt{2}\) is only for an Isosceles right angled triangle {45-45-90} degrees. Not for any other set of angles
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The figure above shows the shape and dimensions of a floor that is to 23 Jun 2019, 06:45
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Bunuel , due to the low hit rate on this question, could you please be quite detailed when presenting your solution?

I feel like many of us seem to miss a quirk in this question.

Best regards,
Chris
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The figure above shows the shape and dimensions of a floor that is to 16 Sep 2023, 23:16
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