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# A rectangular floor is covered by a rug except fo a strip p

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A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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Updated on: 26 Dec 2018, 10:05
2
10
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:46) correct 33% (02:04) wrong based on 385 sessions

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A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn – 2p(m+n)
C) mn – p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

Project PS Butler : Question #102

Originally posted by TheRob on 07 Sep 2009, 06:49.
Last edited by HKD1710 on 26 Dec 2018, 10:05, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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07 Sep 2009, 10:07
5

Area of rug = (m-2p)(n-2p)
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rug.gif [ 3.68 KiB | Viewed 5332 times ]

##### General Discussion
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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Updated on: 06 Aug 2014, 00:37
Q. A rectangular floor is covered by a rug except for a strip p meters wide along each of the four edges. If the floor is m meters by n meters, what is the area of the rug, in square meters?

1. mn-p(m+n)

2. mn-2p(m+n)

3. mn-p^2

4. (m-p)(n-p)

5.(m-2p)(n-2p)

Note: Please solve by explaining the concept.
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Originally posted by royQV on 05 Aug 2014, 22:15.
Last edited by royQV on 06 Aug 2014, 00:37, edited 1 time in total.
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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05 Aug 2014, 22:35
1

Plug in M 100
N 50
P 10.

Correct me if I am wrong.
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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06 Aug 2014, 00:01
royQV wrote:
Q. A rectangular floor is covered by a rug except for a strip p meters wide along each of the four edges. If the floor is m meters by n meters, what is the area of the rug, in square meters?

1. mn-p(m+n)

2. mn-2p(m+n)

3. mn-p^2

4. (m-p)(n-p)

5.(m-2p)(n-2p)

Note: Please solve by explaining the concept.

The OA should be E
Area of the rug is (m-2p)*(n-2p)
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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06 Aug 2014, 00:22
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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06 Aug 2014, 00:39
nikhilbajpai wrote:

It is indeed E- a-rectangular-floor-is-covered-by-a-rug-except-for-a-strip-p-62376.html?fl=similar

Area of floor is m*n
Length of rug = m - 2p (Distance of p on each side)
Width of rug = n - 2p (Distance of p on each side)

Thus area of rug = (m-2p)(n-2p)
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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06 Aug 2014, 19:12
royQV wrote:
Q. A rectangular floor is covered by a rug except for a strip p meters wide along each of the four edges. If the floor is m meters by n meters, what is the area of the rug, in square meters?

1. mn-p(m+n)

2. mn-2p(m+n)

3. mn-p^2

4. (m-p)(n-p)

5.(m-2p)(n-2p)

Note: Please solve by explaining the concept.

Refer diagram below; we require to find area of the pink region

Attachments

rec.png [ 2.91 KiB | Viewed 4837 times ]

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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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29 Jun 2015, 16:37
1. mn-p(m+n) Depending on the size of $$m$$,$$n$$, and $$p$$, the number could be positive or negative.
2. mn-2p(m+n) Again, depending on the size of $$m$$,$$n$$, and $$p$$, the number could be positive or negative
3. mn-p^2 This is only the area in the top corner
4. (m-p)(n-p) Trick answer. Selected if one's coasting through the problem.
5.(m-2p)(n-2p) True, since $$p$$ surrounds all four edges of the rug
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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27 Oct 2015, 13:47
Bunuel , hi, where can i find some questions on similar triangles...?
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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27 Oct 2015, 21:48
saroshgilani wrote:
Bunuel , hi, where can i find some questions on similar triangles...?

Check GEOMETRY tags in our questions banks: viewforumtags.php

Hope it helps.
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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29 Dec 2015, 10:32
A doubt that was running in my mind but was clarified as I solved the sum - do not worry with a square being a rectangle and such special cases. Technically, the area of square is also length multiplied with breadth, just that the two are same and the area resurfaces as side * side
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Re: A rectangular floor is covered by a rug except fo a strip p  [#permalink]

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20 Aug 2019, 09:48
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Re: A rectangular floor is covered by a rug except fo a strip p   [#permalink] 20 Aug 2019, 09:48
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