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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]

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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
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink]

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New post 12 Dec 2012, 08:52
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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]

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New post 06 May 2014, 12:34
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink]

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New post 28 Oct 2014, 17:13
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Bunuel wrote:
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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.


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]

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New post 29 Oct 2014, 02:03
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Segmented the shaded region in 2 as shown below:
Attachment:
Door.png
Door.png [ 5.29 KiB | Viewed 6002 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]

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New post 18 Dec 2015, 08:11
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Re: The front of a 6-foot-by-8-foot rectangular door has brass [#permalink]

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New post 11 Jun 2016, 06:42
Walkabout wrote:
Attachment:
Door.png
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


To solve this problem we can view it as a type of “shaded region” problem, in which we first determine the area of the entire figure and then subtract the area of the unshaded (white) space from the total area to determine the area of the shaded region, which, in this case, is the area of the trim. Let’s start with the area of the entire figure. We see from the diagram that the shape is a rectangle 6 feet by 8 feet. Since the area of a rectangle is width x length, we know:

area = 6 x 8 = 48

We can determine the area of the trim by first finding the area of the white spaces. We can use a diagram to illustrate this:

Image

We can see that, to determine the total area of the two white spaces, we can subtract a total of 2 feet from the 6 foot width and 3 feet from the 8 foot length. Thus, the combined area of the two white spaces is:

(6 – 2) x (8 – 3) = 4 x 5 = 20.

Thus, we know that the area of shaded region, i.e., the trim, is:

48 – 20 = 28

Finally, we can determine the fraction of the door's front surface that is covered by the trim.

Because the area of the trim is 28 and the area of the entire door is 48, the fraction of the door that is covered by the trim is 28/48 = 7/12.

Answer: D
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Re: The front of a 6-foot-by-8-foot rectangular door has brass   [#permalink] 11 Jun 2016, 06:42
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