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# The figure above shows the shape and dimensions of a floor that is to

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Math Expert
Joined: 02 Sep 2009
Posts: 56268
The figure above shows the shape and dimensions of a floor that is to  [#permalink]

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21 Jun 2019, 00:31
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Difficulty:

75% (hard)

Question Stats:

23% (02:57) correct 77% (03:02) wrong based on 22 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

Attachment:

d1.JPG [ 3.95 KiB | Viewed 435 times ]

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Director
Joined: 20 Jul 2017
Posts: 526
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
The figure above shows the shape and dimensions of a floor that is to  [#permalink]

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21 Jun 2019, 04:20
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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 Pls Hit Kudos if you like the solution Attachments 34.png [ 6.3 KiB | Viewed 407 times ] Senior Manager Joined: 12 Sep 2017 Posts: 295 Re: The figure above shows the shape and dimensions of a floor that is to [#permalink] ### Show Tags 21 Jun 2019, 13:38 Dillesh4096 wrote: 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. $780 Attachment: d1.JPG 6m wide roll will cost 30$ 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

Hello Dillesh4096

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

Kind regards!
Director
Joined: 20 Jul 2017
Posts: 526
Location: India
Concentration: Entrepreneurship, Marketing
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Re: The figure above shows the shape and dimensions of a floor that is to  [#permalink]

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21 Jun 2019, 13:46
jfranciscocuencag wrote:
Dillesh4096 wrote:

Hello Dillesh4096

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

Kind regards!

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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Re: The figure above shows the shape and dimensions of a floor that is to  [#permalink]

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23 Jun 2019, 06:45
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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Re: The figure above shows the shape and dimensions of a floor that is to   [#permalink] 23 Jun 2019, 06:45
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