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]

21 Dec 2007, 04:40

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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.

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Re: DS: Angle formed by Diagonal in Rectangle [#permalink]

04 Mar 2011, 10:32

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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: DS: Angle formed by Diagonal in Rectangle [#permalink]

21 Dec 2007, 05:24

GK_Gmat wrote:

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]

21 Dec 2007, 15:28

GK_Gmat wrote:

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]

21 Dec 2007, 16:26

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]

22 Dec 2007, 00:32

Question remains: how do you go about finding the angle (without using tan, cosine, etc.)??

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[#permalink]

22 Dec 2007, 00:58

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]

03 Mar 2011, 21:47

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]

03 Mar 2011, 22:30

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]

03 Mar 2011, 22:36

gmat1220 wrote:

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, 11:13, edited 1 time in total.

Re: DS: Angle formed by Diagonal in Rectangle [#permalink] 03 Mar 2011, 22:36

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