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The area of a rectangle is 80. What is the angle between the

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The area of a rectangle is 80. What is the angle between the [#permalink] New post 21 Dec 2007, 03:40
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The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

(1) The perimeter of the rectangle is 84
(2) The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.
[Reveal] Spoiler: OA
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 21 Dec 2007, 04:24
GK_Gmat wrote:
The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

1. The perimeter of the rectangle is 84
2. The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.



L*W = 80

2*(L+W)=84

2*(80/w + w)=84

w^2 -42w +80 =0

Factorizing, we get

(w-40)(w-2) = 0

w=40 or 2

Therefore, longer side is 40 and shorter is 2, which is easier part as you have mentioned. ( First, yes, the internal angles of a rectangle are 90deg But that wont help you much here)
Neither knowing that the diagonals of the rectangle are of equal length and they bisect each other.

Hmmm.....I am not sure how to proceed in a fast way.... If I could use Trigonometry, we can find the angle.

Anyways, as the angle can be found using both the statements ( i ) and ( ii ), the answer in GMAT DS should be "C".!
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 21 Dec 2007, 14:28
GK_Gmat wrote:
The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

1. The perimeter of the rectangle is 84
2. The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.


I originally said D and I still think its D after looking at LM's approach.

B/c we know the longer and shorter sides in both statements shouldnt the answer be D?
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 [#permalink] New post 21 Dec 2007, 15:26
Expert's post
I also think D.
Both statements alone seem to fix rectangle at an unique configuration giving us the sides and angles.
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 [#permalink] New post 21 Dec 2007, 23:32
Question remains: how do you go about finding the angle (without using tan, cosine, etc.)??
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 [#permalink] New post 21 Dec 2007, 23:58
i think here we should say yes or no.
since you know the values of two sides of a right traingle it is easy to find using cos or tan tables. but in gmat u do not need to do so if it is DS.

D
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 03 Mar 2011, 20:47
This doesnt seem like a typical GMAT question. They usually dont expect you to know that you can solve this with Trigonometry.
I saw this question on M23, question 24.
This is the explanation which i dont agree with

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

Statement (2) by itself is sufficient. We can find the sides of the rectangle (40 and 2).
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 03 Mar 2011, 21:30
If all the sides of the triangle are known, the shape is fixed. If the shape is fixed the angles are fixed. I dont think gmat really cares the means you are going to use, to determine the solution. Whether you can determine is all that matters.
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 03 Mar 2011, 21:36
gmat1220 wrote:
If all the sides of the triangle are known, the shape is fixed. If the shape is fixed the angles are fixed. I dont think gmat really cares the means you are going to use, to determine the solution. Whether you can determine is all that matters.


You can use law of cosines to calculate the angles.

But i am still not convinced this is a standard question.

Last edited by mbafall2011 on 04 Mar 2011, 10:13, edited 1 time in total.
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Re: DS: Angle formed by Diagonal in Rectangle [#permalink] New post 04 Mar 2011, 09:32
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GK_Gmat wrote:
The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

1. The perimeter of the rectangle is 84
2. The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.


I think the answer is D after looking at the problem:

I) 80 = W*L
P=2L+2W
84=2L+2W

80/w = L

84 = 2w+2(80/w)
42= w+(80/w)
42=(w/w)(w/1)+(80/W)
42=(w^2+80)/W
42w=(w^2)+80
0=(w^2)-42w+80
factor: (w-40)(w-2)
Longer = 40 Shorter = 2, angle can be obtained: I) sufficient

II) repeats information you already solved for validating your solution and not contradicting itself, sufficient

Answer: D
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 19 Jan 2014, 06:20
GK_Gmat wrote:
The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

(1) The perimeter of the rectangle is 84
(2) The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.


I got D as well cause I could figure out that both statements provided same info but I don't quite get the problem/ What are we asked for? The angle between the diagonals and its longest side, isn't it always 45? The diagonal should bisect the angle no?

Could anybody please clarify?
Thanks
Cheers!
J :)
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 19 Jan 2014, 09:47
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jlgdr wrote:
GK_Gmat wrote:
The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?

(1) The perimeter of the rectangle is 84
(2) The shorter side of the rectangle is 2


Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.


I got D as well cause I could figure out that both statements provided same info but I don't quite get the problem/ What are we asked for? The angle between the diagonals and its longest side, isn't it always 45? The diagonal should bisect the angle no?

Could anybody please clarify?
Thanks
Cheers!
J :)


Not necessarily. The diagonal of a square bisects the angle but not all rectangles are squares.
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 29 Jan 2014, 10:18
Once we know all the sides, is there a way to find the two missing angles? Could anybody please explain how?

If it is not necessary to know how, please just confirm that when knowing the three sides of a right angled triangle it is enough information to find the missing angles (by trigonometry I guess).

Thank you in advance,
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 29 Jan 2014, 10:49
I'm also interested to know the solution to this problem, because I had to rely on sin/cos to "prove" that the question could technically be solved. Plus, the fact that two statements gave the same piece of information, given that they couldn't contradict, I picked D.

Waiting for the solution from the experts.
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 29 Jan 2014, 21:56
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Abdul29 wrote:
I'm also interested to know the solution to this problem, because I had to rely on sin/cos to "prove" that the question could technically be solved. Plus, the fact that two statements gave the same piece of information, given that they couldn't contradict, I picked D.

Waiting for the solution from the experts.


You don't need to solve this question! It's a waste of time. You are asked not to calculate a value but to determine whether you are able to do so with the information supplied.
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Re: The area of a rectangle is 80. What is the angle between the [#permalink] New post 29 Jan 2014, 22:00
Bunuel wrote:
Abdul29 wrote:
I'm also interested to know the solution to this problem, because I had to rely on sin/cos to "prove" that the question could technically be solved. Plus, the fact that two statements gave the same piece of information, given that they couldn't contradict, I picked D.

Waiting for the solution from the experts.


You don't need to solve this question! It's a waste of time. You are asked not to calculate a value but to determine whether you are able to do so with the information supplied.


True, on the real test I would have picked (D) and moved on.
Re: The area of a rectangle is 80. What is the angle between the   [#permalink] 29 Jan 2014, 22:00
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