A rectangular room has the rectangular shaped rug...
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A rectangular room has the rectangular shaped rug shown as above figure such that the rug's area is 120 square feet and its lenght is 2 feet longer than its width. If the uniform width between the rug and room is 2 feet, whta is the area of the region uncovered by the rug (shaded region), in square feet?
A. 32
B. 36
C. 40
D. 46
E. 104
The OA is E.
I know that the area of a rectangle can be determinated by A=L*W and I know that rug's area is 120, then
120=L*W and also I know that the rug has L=2*W, teherefore, its width will be root(60) and its lenght will be L=2*root(60).
Experts, I need your help with this PS question, I don't know how can I determinate the area of the shaded region, I don't know how can I continue with the solving of this question. Thanks!
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The rug's area is 120 square feet and its length is 2 feet longer than its widthAAPL wrote:
A rectangular room has the rectangular shaped rug shown as above figure such that the rug's area is 120 square feet and its length is 2 feet longer than its width. If the uniform width between the rug and room is 2 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
A. 32
B. 36
C. 40
D. 46
E. 104
Let n = rug's width
So n +2 = rug's length
Area of rectangular rug = (length)(width)
So: 120 = (n)(n+2)
Expand: 120 = n² + 2n
Rearrange: n² + 2n - 120 = 0
Factor: (n + 12)(n - 10) = 0
So, EITHER n = -12, OR n = 10
Since the width must be POSITIVE, we know that n = 10
So, the rug's width = 10 feet, and the rug's length = 12 feet,
AREA of rug = 120
Uniform width between the rug and room is 2 feet
So, there's a 2-foot gap between each side of the rug and the walls of the room.
So, the ROOM'S width = 10 + 2 + 2 feet, and the ROOM'S length = 12 + 2 + 2 feet.
In other words, the ROOM'S DIMENSIONS are 14 feet by 16 feet
AREA of room = (14)(16) = 224
What is the area of the region uncovered by the rug (shaded region), in square feet?
Uncovered area = (area of ROOM) - (area of RUG)
= 224 - 120
= 104
= E
Cheers,
Brent
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Hi AAPL,
We're told that a rectangular room has the rectangular shaped rug such that the rug's area is 120 square feet and its length is 2 feet longer than its width. In addition, the uniform width between the rug and room is 2 feet. We're asked for the area of the region NOT covered by the rug (in square feet).
To start, since the area of the rug is 120 - and the length is 2 feet greater than the width - we're looking for two dimensions that DIFFER by 2 and have a product of 120. Since the product ends in a 0, one of the dimensions will end in either a 5 or a 0. Without too much trouble, you'll find that 10 feet x 12 feet are the dimensions of the rug.
Since the uniform width between the rug and the walls is 2 feet - and each dimension includes 2 'uniform widths', we know that the dimensions of the room are (10+4) feet x (12+4) feet.... 14 feet x 16 feet.
Area of the room = (14)(16) = 224 feet
Area of the rug = (10)(12) = 120 feet
Uncovered area = 224 - 120 = 104 feet
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that a rectangular room has the rectangular shaped rug such that the rug's area is 120 square feet and its length is 2 feet longer than its width. In addition, the uniform width between the rug and room is 2 feet. We're asked for the area of the region NOT covered by the rug (in square feet).
To start, since the area of the rug is 120 - and the length is 2 feet greater than the width - we're looking for two dimensions that DIFFER by 2 and have a product of 120. Since the product ends in a 0, one of the dimensions will end in either a 5 or a 0. Without too much trouble, you'll find that 10 feet x 12 feet are the dimensions of the rug.
Since the uniform width between the rug and the walls is 2 feet - and each dimension includes 2 'uniform widths', we know that the dimensions of the room are (10+4) feet x (12+4) feet.... 14 feet x 16 feet.
Area of the room = (14)(16) = 224 feet
Area of the rug = (10)(12) = 120 feet
Uncovered area = 224 - 120 = 104 feet
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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AAPL wrote:
A rectangular room has the rectangular shaped rug shown as above figure such that the rug's area is 120 square feet and its lenght is 2 feet longer than its width. If the uniform width between the rug and room is 2 feet, whta is the area of the region uncovered by the rug (shaded region), in square feet?
A. 32
B. 36
C. 40
D. 46
E. 104
The OA is E.
I know that the area of a rectangle can be determinated by A=L*W and I know that rug's area is 120, then
120=L*W and also I know that the rug has L=2*W, teherefore, its width will be root(60) and its lenght will be L=2*root(60).
Experts, I need your help with this PS question, I don't know how can I determinate the area of the shaded region, I don't know how can I continue with the solving of this question. Thanks!
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- Master | Next Rank: 500 Posts
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- Joined: Wed Nov 29, 2017 4:38 pm
- Thanked: 14 times
since the area of rug is 120 with given length longer by 2 feet than its breadth ,one can easily visuallise thatAAPL wrote:
A rectangular room has the rectangular shaped rug shown as above figure such that the rug's area is 120 square feet and its lenght is 2 feet longer than its width. If the uniform width between the rug and room is 2 feet, whta is the area of the region uncovered by the rug (shaded region), in square feet?
A. 32
B. 36
C. 40
D. 46
E. 104
The OA is E.
I know that the area of a rectangle can be determinated by A=L*W and I know that rug's area is 120, then
120=L*W and also I know that the rug has L=2*W, teherefore, its width will be root(60) and its lenght will be L=2*root(60).
Experts, I need your help with this PS question, I don't know how can I determinate the area of the shaded region, I don't know how can I continue with the solving of this question. Thanks!
the length must be 12 and breadth 10.
since the uniform width between room and the rug is 2 feet, the average length of room and rug would be 12+2 =14 feet
and average breadth would be 10+2 =12 feet.
thus the perimeter along the average length and breadth would be (14+12)*2=52
Area between the room and rug = average perimeter x uniform width
=52*2= 104
Hence E is the correct option