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# What is the area of the rectangular region above?

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Senior Manager
Joined: 18 Oct 2010
Posts: 409
What is the area of the rectangular region above? [#permalink]

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24 Feb 2011, 10:39
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Question Stats:

75% (00:44) correct 25% (00:47) wrong based on 183 sessions

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What is the area of the rectangular region above?

(1) l + w = 6.
(2) d^2 = 20

[Reveal] Spoiler:
Attachment:

untitled.PNG [ 1.94 KiB | Viewed 6407 times ]
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jan 2018, 20:00, edited 2 times in total.
Edited the question
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Joined: 20 Dec 2010
Posts: 1945
Re: What is the area of the rectangular region above? [#permalink]

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24 Feb 2011, 10:46
3
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(1)
$$l+w = 6$$
$$(l+w)^2 = l^2+w^2+2w*l=36$$
$$w*l=\frac{36-l^2-w^2}{2}$$
Not Sufficient.

(2)
$$d^2=l^2+w^2=20$$
Not Sufficient.

Combining both;
$$w*l=\frac{36-(l^2+w^2)}{2}$$
$$w*l=\frac{36-20}{2}$$
$$w*l=\frac{16}{2}$$
$$w*l=8$$(Area is w*l)

Sufficient.

Ans: "C"
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Re: What is the area of the rectangular region above? [#permalink]

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24 Feb 2011, 10:49
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?
Math Expert
Joined: 02 Sep 2009
Posts: 43853
What is the area of the rectangular region above? [#permalink]

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24 Feb 2011, 11:10
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What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html
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Re: What is the area of the rectangular region above? [#permalink]

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24 Feb 2011, 11:12
1
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Thanks for letting me know Bunuel. I shall follow the rules henceforth!!
I actually thought b could be the right answer here. I made a wrong assumption : diag of a rect make 45 degrees!
Manager
Joined: 14 Feb 2011
Posts: 181
Re: What is the area of the rectangular region above? [#permalink]

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08 Mar 2011, 23:19
Lolaergasheva wrote:
What is the area of the rectangular region ?
(1) l + w = 6
(2) d^2 = 20

Area of rectangular region is given by $$l*w$$.

Statement 1 gives us,$$l+w=6$$, but l and w can take any values, so insufficient

Statement 2 gives us $$d^2 = 20$$ . Assuming that d refers to length of diagonal, we have $$d^2 = l^2 + w^2 = 20$$. Again l and w can take multiple values, so insufficient.

Combining 1 and 2,

we get $$l+w=6$$ ... (1)

and $$l^2 + w^2 = 20$$.... (2)

Squaring both sides of (1), we get

so, $$l^2 + w^2 + 2l*w = 36$$

Putting $$l^2 + w^2 = 20$$ in above we get $$2l*w = 16$$ or $$l*w = 8$$

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Re: What is the area of the rectangular region above? [#permalink]

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07 Sep 2015, 06:28
1
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Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

What is the area of the rectangular region above?

(1) l + w = 6. Not sufficient to get the value of .
(2) d^2 = 20

In the original condition we have 2 variables for the rectangle(width, length) and thus we need 2 variables to match the number of variables and equations. Since there is 1 each in 1) and 2), C is likely the answer.
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Re: What is the area of the rectangular region above? [#permalink]

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30 Jan 2018, 18:03
Bunuel wrote:
heygirl wrote:
What is the area of a rectangle with length l and width w?
(1)l+w=6
(2)d^2=20(d is the diagonal)

Make sure you type the question in exactly as it was stated from the source. Yuo should not reword or/and shorten the questions.

Original question:

Attachment:
untitled.PNG
What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel, I screwed up and assumed I was to use the 30:60:90 triangle rule for statement #2 (since it's a rectangle).

How am I supposed to know that rule won't work for this question? Is it because d^2 = 20 -> d= 4 square root 5, but not 4 square root 3?
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Joined: 02 Sep 2009
Posts: 43853
Re: What is the area of the rectangular region above? [#permalink]

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30 Jan 2018, 20:07
OCDianaOC wrote:
Bunuel wrote:
heygirl wrote:
What is the area of a rectangle with length l and width w?
(1)l+w=6
(2)d^2=20(d is the diagonal)

Make sure you type the question in exactly as it was stated from the source. Yuo should not reword or/and shorten the questions.

Original question:

Attachment:
untitled.PNG
What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel, I screwed up and assumed I was to use the 30:60:90 triangle rule for statement #2 (since it's a rectangle).

How am I supposed to know that rule won't work for this question? Is it because d^2 = 20 -> d= 4 square root 5, but not 4 square root 3?

Knowing only the length of a diagonal of a rectangle does not allow to find its adjacent angles. You can squeeze or stretch a rectangle with any length of a diagonal along one of its sides to get any adjacent lengths from 0 to 90 not inclusive.
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Re: What is the area of the rectangular region above?   [#permalink] 30 Jan 2018, 20:07
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