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To cover the floor of an entry hall, a 1′ * 12′ strip of car
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24 Mar 2020, 00:06
24 Mar 2020, 00:06
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To cover the floor of an entry hall, a 1′ * 12′ strip of carpet is cut into two pieces, shown as the shaded strips in the figure above, and each piece is connected to a third carpet piece as shown. If the 1′ strips run parallel to each other, what is the total area of the carpeted floor, in square feet?
(A) 46
(B) 48
(C) 52.5
(D) 56
(E) 60
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Re: To cover the floor of an entry hall, a 1′ * 12′ strip of car
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12 Feb 2021, 12:56
12 Feb 2021, 12:56
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GeminiHeat wrote:
Attachment:
11.jpg
To cover the floor of an entry hall, a 1′ * 12′ strip of carpet is cut into two pieces, shown as the shaded strips in the figure above, and each piece is connected to a third carpet piece as shown. If the 1′ strips run parallel to each other, what is the total area of the carpeted floor, in square feet?
(A) 46
(B) 48
(C) 52.5
(D) 56
(E) 60
Is it option E, 60?
Explanation:
Strip of Carpet has Length as 12 ft and width as 1 ft
Let us cut this strip into 2 pieces of A ft and (12 - A) ft
Area of Upper strip = A ft x 1 ft = A\(ft^2\)
Area of Lower strip = (12 - A) ft x 1 ft = (12 - A) \(ft^2\)
As we can see, height of the Middle part is 8 ft (10 - 1 - 1)
So, Area of Middle part = \(\frac{1}{2}\) x [A + (12 - A)] x 8 = \(\frac{1}{2}\) x 12 x 8 = 48 \(ft^2\)
Total Area = Area of Upper strip + Area of Middle part + Area of Lower strip
Total Area = A + (12 - A) + 48 = 12 + 48 = 60 \(ft^2\)
Hence, option E
To cover the floor of an entry hall, a 1′ * 12′ strip of car
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13 Feb 2021, 09:15
13 Feb 2021, 09:15
2
Hi,
Although the figure looks like a trapezium we can draw it like a rectangle, as we are not given any definite dimensions. It would make the work easier, to understand as well as to interpret.
Now, as we have a strip of 1'*12', we can divide it into two equal parts, and assume the breadth of the rectangle to be 6'
Thus, we know the area of the two rectangular carpet will be 1'*6'=6; 6+6=12 inches.
Area of the carpet strip=12 inches
In order to find the area of the middle section i.e. area of third carpet, we have the dimensions in feet.
12 inches= 1 Feet
Thus, Total length of the figure= 12*10=120 inches
And as some region is covered by another carpet, we can subtract it= 120-2=118 '
As we know the length & Breadth of the rectangle (Middle section) are 118*6= 708'
Area of the middle section=708
708'+12'=720'
720' inches is the area of the complete figure.
Converting inches into feet= 720/12=60 Feet
Thus, Area of the figure= 60 Feet.
IMO E
P.S.: Although this might look a bit tedious but once you understand this it would be easy and a quick to solve. And the figure could be interpreted in any way as we are not asked to use any said angles or dimensions.
Hope this helps!
Although the figure looks like a trapezium we can draw it like a rectangle, as we are not given any definite dimensions. It would make the work easier, to understand as well as to interpret.
Now, as we have a strip of 1'*12', we can divide it into two equal parts, and assume the breadth of the rectangle to be 6'
Thus, we know the area of the two rectangular carpet will be 1'*6'=6; 6+6=12 inches.
Area of the carpet strip=12 inches
In order to find the area of the middle section i.e. area of third carpet, we have the dimensions in feet.
12 inches= 1 Feet
Thus, Total length of the figure= 12*10=120 inches
And as some region is covered by another carpet, we can subtract it= 120-2=118 '
As we know the length & Breadth of the rectangle (Middle section) are 118*6= 708'
Area of the middle section=708
708'+12'=720'
720' inches is the area of the complete figure.
Converting inches into feet= 720/12=60 Feet
Thus, Area of the figure= 60 Feet.
IMO E
P.S.: Although this might look a bit tedious but once you understand this it would be easy and a quick to solve. And the figure could be interpreted in any way as we are not asked to use any said angles or dimensions.
Hope this helps!
