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The front of a 6-foot-by-8-foot rectangular door has brass

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The front of a 6-foot-by-8-foot rectangular door has brass [#permalink] New post 12 Dec 2012, 07:45
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64% (02:34) correct 36% (01:27) wrong based on 490 sessions
Attachment:
Door.png
Door.png [ 6.35 KiB | Viewed 7261 times ]
The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim?

(A) 13/48
(B) 5/12
(C) 1/2
(D) 7/12
(E) 5/8
[Reveal] Spoiler: OA
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink] New post 12 Dec 2012, 07:52
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The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim?

(A) 13/48
(B) 5/12
(C) 1/2
(D) 7/12
(E) 5/8

First let's find the area of unshaded region.

The two unshaded regions have a width of 4 feet: 6 feet minus 1 foot wide trim on each side.
The two unshaded regions have a height of 5 feet: 8 feet minus 1 foot at the top, 1 foot in the middle and 1 foot at the bottom.

Thus the area of the two unshaded regions is 4*5=20 square feet.

Therefore, the area of the trim is 6*8-20=28 square feet, which is 28/48=7/12 of the total area.

Answer: D.

Hope it's clear.
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink] New post 29 Oct 2014, 01:03
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Segmented the shaded region in 2 as shown below:
Attachment:
Door.png
Door.png [ 5.29 KiB | Viewed 2843 times ]


Yellow region area = 2 * 8*1 = 16

Pink region area = 3 * 4*1 = 12

Total shaded region = 28

Total frame area = 8*6 = 48

Ratio \(= \frac{28}{48} = \frac{7}{12}\)

Answer = D
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink] New post 28 Oct 2014, 16:13
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Bunuel wrote:
Image
The front of a 6-foot-by-8-foot rectangular door has brass rectangular trim, as indicated by the shading in the figure above. If the trim is uniformly 1 foot wide, what fraction of the door's front surface is covered by the trim?

(A) 13/48
(B) 5/12
(C) 1/2
(D) 7/12
(E) 5/8

First let's find the area of unshaded region.

The two unshaded regions have a width of 4 feet: 6 feet minus 1 foot wide trim on each side.
The two unshaded regions have a height of 5 feet: 8 feet minus 1 foot at the top, 1 foot in the middle and 1 foot at the bottom.

Thus the area of the two unshaded regions is 4*5=20 square feet.

Therefore, the area of the trim is 6*8-20=28 square feet, which is 28/48=7/12 of the total area.

Answer: D.

Hope it's clear.


Thank you for this. I accidently chose the trap answer of \(\frac{5}{12}\), and found the area of the door not covered by trim
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink] New post 06 May 2014, 11:34
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Re: The front of a 6-foot-by-8-foot rectangular door has brass   [#permalink] 06 May 2014, 11:34
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