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# What is the area of the rectangular region above?

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What is the area of the rectangular region above? [#permalink]  24 Feb 2011, 10:39
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:40) correct 22% (00:48) wrong based on 54 sessions
Attachment:

untitled.PNG [ 1.94 KiB | Viewed 2937 times ]
What is the area of the rectangular region above?

(1) l + w = 6. Not sufficient to get the value of .
(2) d^2 = 20
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Feb 2012, 13:10, edited 1 time in total.
Edited the question
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Re: OG Quant review book question [#permalink]  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: OG Quant review book question [#permalink]  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)?
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Re: OG Quant review book question [#permalink]  24 Feb 2011, 11:10
2
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Expert's post
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 [ 1.94 KiB | Viewed 2831 times ]
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:
need-some-help-on-this-ds-question-105414.html
og12-d48-102246.html
one-more-geometry-96381.html
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Re: OG Quant review book question [#permalink]  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!
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Re: OG Quant review book question [#permalink]  24 Feb 2011, 16:37
Both Bunuel and fluke approaches were great. Thanks for that!
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Re: d/s geometry [#permalink]  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 $$l*w = 8$$

Re: d/s geometry   [#permalink] 08 Mar 2011, 23:19
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