The front of a 6 foot by 8 foot rectangular door has brass rectangular trim.If the trim is as 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
OG -12 113 Problem
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The area of the trim is equal to the total area of the door minus the area of the portions not covered by trim.
The total area is easy: 8 * 6 = 48 sq ft
The two portions without trim have a width of 4 feet because the trim is 1 foot wide on each side. Of the 8 feet in height, 3 feet are taken up the by the one foot wide portions of trim: one foot at the top, one foot at the bottom, and one foot in the middle of the two untrimmed portions. This means that our portions without trim have a height of 8 - 3 = 5 feet. Thus, the total area of the portions without trim is 4*5 = 20 sq feet.
This leaves 48 - 20 = 28 sq feet for the area of the trim. The fraction is then 28/48, or 7/12.
The total area is easy: 8 * 6 = 48 sq ft
The two portions without trim have a width of 4 feet because the trim is 1 foot wide on each side. Of the 8 feet in height, 3 feet are taken up the by the one foot wide portions of trim: one foot at the top, one foot at the bottom, and one foot in the middle of the two untrimmed portions. This means that our portions without trim have a height of 8 - 3 = 5 feet. Thus, the total area of the portions without trim is 4*5 = 20 sq feet.
This leaves 48 - 20 = 28 sq feet for the area of the trim. The fraction is then 28/48, or 7/12.
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Solution:theachiever wrote:The front of a 6 foot by 8 foot rectangular door has brass rectangular trim.If the trim is as 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 sq. ft.
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:
We see that, to determine the total area of the two white spaces, we 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 sq. ft.
Thus, we know that the area of shaded region, i.e., the trim, is:
48 - 20 = 28 sq. ft.
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 sq. ft. and the area of the entire door is 48 sq. ft., the fraction of the door that is covered by the trim is 28/48 = 7/12.
Answer: D
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It is not mentioned anywhere in the question about the middle trim.
Is there missed diagram of door face.
If there is no middle trim then answer is 1/2
door area = 6*8 = 48
area with trim 4*6 = 24
area of trim = 48-24 = 24
ration = 24/48 = 1/2
Is there missed diagram of door face.
If there is no middle trim then answer is 1/2
door area = 6*8 = 48
area with trim 4*6 = 24
area of trim = 48-24 = 24
ration = 24/48 = 1/2