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Math Expert V
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Difficulty:   45% (medium)

Question Stats: 66% (01:30) correct 34% (01:59) wrong based on 137 sessions

HideShow timer Statistics If 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

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Math Expert V
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Official Solution:

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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1
I think this question is not helpful.
Understood that you can find the sides of the rectangle, but how do you find the ANGLE between the diagonal and the longer side of the rectangle, as the question stem asks?
Math Expert V
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KPMM07 wrote:
I think this question is not helpful.
Understood that you can find the sides of the rectangle, but how do you find the ANGLE between the diagonal and the longer side of the rectangle, as the question stem asks?

Finding the angles is not our aim. The aim is to determine whether we CAN find them.
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Bunuel wrote:
KPMM07 wrote:
I think this question is not helpful.
Understood that you can find the sides of the rectangle, but how do you find the ANGLE between the diagonal and the longer side of the rectangle, as the question stem asks?

Finding the angles is not our aim. The aim is to determine whether we CAN find them.

It is clearly asked " What Is the angle"?? So shudnt we return a value in the answer ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
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Omkar.kamat wrote:
Bunuel wrote:
KPMM07 wrote:
I think this question is not helpful.
Understood that you can find the sides of the rectangle, but how do you find the ANGLE between the diagonal and the longer side of the rectangle, as the question stem asks?

Finding the angles is not our aim. The aim is to determine whether we CAN find them.

It is clearly asked " What Is the angle"?? So shudnt we return a value in the answer ??

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. The actually finding the value is not necessary. The fact that we can find the value and that's it will be unique is enough.
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3
I think this is good question:

This question tests the understanding of very basic concept:

Below ae the 3 ways in which we can draw a unique triangle :
1: 3 side lengths are known.
2: 2 sides and an angle are known.
3: 2 angle and a 1 side are known.

For 2 and 3 you need a specific angle. Check this http://www.mathwarehouse.com/triangle-calculator/online.php

Now this question satisfies 1st criteria. if there is only 1 triangle then there will be one unique combination of angles for that set of sides.

So Ans D

Thanks.
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Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?
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dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.
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Hi All,

Must Known for GMAT,

IF YOU CAN DRAW THE FIGURE, IT MEANS THAT YOU KNOW ALL PROPERTIES

From Stem : $$width * length = 80$$

Statement 1 : $$width + length = 42$$

We have two equations, with two variables so we can solve and find the two sides : 40 and 2 ==> SUFFICIENT

Statement 2 : Shorter side is 2

So we have $$2 * length = 80$$
Therefore length = 40 and thus we can draw the figure and know all the angles. ==> SUFFICIENT

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dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Hi,
Just to satisfy the query of many friends -
Knowing all the sides of a triangle helps in identifying the angle between any two sides. How : Here it follows:
Calculate the area using Heros Formula : Area= √s(s-a)(s-b)(s-c) where s = sum of all the sides / 2 and a,b,c are the length of the sides. ------ (1)
Also Area = 1/2 ab sinx where x is angle between side a and b. -----(2)
Equate (1) & (2) to extract the value of sinx or x.
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I think this is a high-quality question and I don't agree with the explanation. When we solve wstatement-1, we will get 2 values either (l,b) = (40,2) or (2,40), so accordingly angle will also be different. So, not sufficient. Answer must be option B. Kindly correct if I am wrong.
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mohitpoddar wrote:
I think this is a high-quality question and I don't agree with the explanation. When we solve wstatement-1, we will get 2 values either (l,b) = (40,2) or (2,40), so accordingly angle will also be different. So, not sufficient. Answer must be option B. Kindly correct if I am wrong.

We need to find the angle between the diagonal of the rectangle and its longer side. So, it does not matter whether it's (40,2) or (2,40). In any case we should find the angle between the diagonal and the side of length 40.
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Bunuel wrote:
If 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

Area of rectangle = 80
Let length of rectangle = L
and breadth of rectangle = B
=> LB = 80

1. Perimeter =84
=> 2(L+B) = 84
=> L+B = 42
=> B = 42-L

Now , L* (42-L) = 80
=> L^2 - 42L +80 = 0
=> L^2 - 40L - 2L +80 = 0
=> (L-2)(L-40) = 0
=> L = 2 , 40
If Length = 2 , then breadth = 40 and vice versa

Now , diagonal can be calculated using Pythagoras theorem .
If we know sides of a triangle , we can calculate the angle using trigonometry.
Sufficient

(2) The shorter side of the rectangle is 2
Sufficient - same as B = 2 and L = 40

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I like this Magoosh explanation in regards to determining the uniqueness of a triangle. In short, if we can determine unique values for SAS, SSS, and etc (see link for full list), then we can determine everything about a triangle since we are essentially breaking the problem down into two triangles.

https://magoosh.com/gmat/2012/gmat-data ... nce-rules/
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Hi,

Statement 1 gives L=40 or 2 B= 2 or 40. Does not changing length and breadth impact the angle?
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Sanjay2043 wrote:
Hi,

Statement 1 gives L=40 or 2 B= 2 or 40. Does not changing length and breadth impact the angle?

Explained above:

We need to find the angle between the diagonal of the rectangle and its longer side. So, it does not matter whether it's (40,2) or (2,40). In any case we should find the angle between the diagonal and the side of length 40.
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Bunuel wrote:
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.

Hi Bunuel,

1. I guess this is true for parallelograms and polygons as well? That knowing the sides is enough to know the angles. I guess Yes , because if we actually start drawing it on paper, we will be able to measure the angles with a protractor?

2. Another question, what if it was a PS question and we actually have to find the angles. I know trigo so I can use that but how do you do it without trigo? Is the ratio of angles of a triangle equal to the ratio of opp sides in all cases?
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abhishek911 wrote:
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.

Hi Bunuel,

1. I guess this is true for parallelograms and polygons as well? That knowing the sides is enough to know the angles. I guess Yes , because if we actually start drawing it on paper, we will be able to measure the angles with a protractor?

2. Another question, what if it was a PS question and we actually have to find the angles. I know trigo so I can use that but how do you do it without trigo? Is the ratio of angles of a triangle equal to the ratio of opp sides in all cases?

1. Yes, it's true for convex polygons.

2. For PS either you won't be asked such question or it would be special triangle involved (30-60-90, 45-45-90).
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Bunuel wrote:
Official Solution:

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

how did you find this? Can't sides be fractions? Re: M23-24   [#permalink] 16 Nov 2017, 07:51

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