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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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New post 12 Dec 2012, 08:45
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Door.png
Door.png [ 6.35 KiB | Viewed 17850 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
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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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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.
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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 12238 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 28 Oct 2014, 17:13
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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]

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New post 11 Jun 2016, 06:42
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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]

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New post 27 Oct 2017, 09:12
PareshGmat wrote:
Segmented the shaded region in 2 as shown below:
Attachment:
Door.png


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


I solved the problem in the same way. IMO the most comprehensive and quick way!
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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 31 Mar 2018, 05:33
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.


Guys i simply counted total 7 shaded lines. so i chose 7/12 :) is my approach correct ? :)
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The front of a 6-foot-by-8-foot rectangular door has brass  [#permalink]

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New post 31 Mar 2018, 16:36
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dave13 wrote:
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

Answer: D.


Guys i simply counted total 7 shaded lines. so i chose 7/12 :) is my approach correct ? :)

dave13 , I doubt that approach is correct . . . because we need a part-whole relationship where all the parts are the same size and I cannot see how counting segments ("lines") achieves same-size parts.

And - which seven segments did you count? (There are a lot of ways to divide the door 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 01 Apr 2018, 02:31
[/quote]

Guys i simply counted total 7 shaded lines. so i chose 7/12 :) is my approach correct ? :)[/quote]
dave13 , I doubt that approach is correct . . . because we need a part-whole relationship where all the parts are the same size and I cannot see how counting segments ("lines") achieves same-size parts.

And - which seven segments did you count? (There are a lot of ways to divide the door trim. :-) )[/quote]

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

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New post 01 Apr 2018, 06:50
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Hi dave13

As generis already pointed out, the approach you have used is not correct.

The right way to solve this problem will be as follow:

The solid door with dimensions 6ft by 8ft will have an area of 48ft.

Attachment:
Door.png
Door.png [ 8.58 KiB | Viewed 1617 times ]


The brass part shaded in black(with a uniform thickness or width of 1 ft) will cover an
area of 8*1 or 8 ft for shaded regions 1 and 2 have an area of 2*8 = 16ft.

Similarly, the three horizontal regions(3,4, and 5), each with an area of 4*1 or 4 ft will
have an area of 3*4 = 12ft

Hence, the brass part will have an area of 16 + 12 = 28 ft

Therefore, the ratio is \(\frac{28}{48} = \frac{7}{12}\) (Option D)

Hope this helps you!
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