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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, 11:39
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80% (01:26) correct 20% (00:52) wrong based on 2 sessions
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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, 14:10, edited 1 time in total.
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Re: OG Quant review book question [#permalink]  24 Feb 2011, 11:46
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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, 12:10
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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 1198 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).

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Re: OG Quant review book question [#permalink]  24 Feb 2011, 12:12
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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, 11:49
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, 17:37
Both Bunuel and fluke approaches were great. Thanks for that!
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Re: d/s geometry [#permalink]  09 Mar 2011, 00:19
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] 09 Mar 2011, 00:19
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