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A rectangular room has the rectangular shaped rug...

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by AAPL » Mon Dec 11, 2017 7:26 am
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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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by Brent@GMATPrepNow » Mon Dec 11, 2017 8:17 am
AAPL wrote:Image

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
The rug's area is 120 square feet and its length is 2 feet longer than its width
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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Mon Dec 11, 2017 9:14 pm
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
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by GMATWisdom » Tue Dec 12, 2017 7:10 am
AAPL wrote:Image

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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by GMATWisdom » Tue Dec 12, 2017 7:15 am
AAPL wrote:Image

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!
since the area of rug is 120 with given length longer by 2 feet than its breadth ,one can easily visuallise that
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
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