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# Area of a rectangle is 80 What is the angle between the

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CEO
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Area of a rectangle is 80 What is the angle between the [#permalink]

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23 Oct 2007, 12:42
Area of a rectangle is 80
What is the angle between the diagonal of the rectangle and its longer side?

1. perimeter is 84
2. shorter side of rectangle is 2
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Location: Berkeley, CA
Schools: Berkeley-Haas MBA
WE 1: Investment Management (fund of funds)
WE 2: Private Equity (\$2bn generalist fund)
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Re: DS - Area of a Rectangle [#permalink]

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23 Oct 2007, 12:48
bmwhype2 wrote:
Area of a rectangle is 80
What is the angle between the diagonal of the rectangle and its longer side?

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

If x is the shorter side
and y is the longer side,

we simply need to find out values of x and y, and angle = tan(inv) x/y

question states: xy = 80

st1. x + y = 84. This gives us 2 eqns and 2 variables, so we can find the values of x and y. SUFF

st2. Since x=2, y=40. we know values of x and y, so we know angle. SUFF

CEO
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Re: DS - Area of a Rectangle [#permalink]

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23 Oct 2007, 13:32
stopper5 wrote:
bmwhype2 wrote:
Area of a rectangle is 80
What is the angle between the diagonal of the rectangle and its longer side?

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

If x is the shorter side
and y is the longer side,

we simply need to find out values of x and y, and angle = tan(inv) x/y

question states: xy = 80

st1. x + y = 84. This gives us 2 eqns and 2 variables, so we can find the values of x and y. SUFF

st2. Since x=2, y=40. we know values of x and y, so we know angle. SUFF

Is there another way to solve this? I dont think TAN, SINE. COSINE are tested on the gmat.
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23 Oct 2007, 14:17
since :

x*y = 80 and 2(x+y) = 84 then:

x = 80/y

2(x+y) = 84

x+y = 42

80/y+y = 42

y^2-42y+80 = 0

(y-2)(y-40) = 0

y can be 2 or 40 and x can be 40 or 2.

knowing that the shorter side is 2 will suffice

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23 Oct 2007, 14:26
killersquirrel,

my calculations are similiar to what you did but then i saw the question which asks about angle. even if you find the diagonal you will need trig to find the angle.

mayb that's why its just a DS question and not a PS.

I got the answer to my question while i was typing this....nm
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20 Dec 2007, 15:05
OA is D.

The angle is dependent on the width.
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20 Dec 2007, 19:17
from statement 1, you get two values .... how is that sufficient ?
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Re: DS - Area of a Rectangle [#permalink]

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21 Dec 2007, 22:33
bmwhype2 wrote:
Area of a rectangle is 80
What is the angle between the diagonal of the rectangle and its longer side?

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

http://www.gmatclub.com/forum/t57397
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22 Dec 2007, 00:34
KillerSquirrel wrote:
since :

x*y = 80 and 2(x+y) = 84 then:

x = 80/y

2(x+y) = 84

x+y = 42

80/y+y = 42

y^2-42y+80 = 0

(y-2)(y-40) = 0

y can be 2 or 40 and x can be 40 or 2.

knowing that the shorter side is 2 will suffice

KS, can you please explain how knowing the length of the shorter side (or of both the shorter side and the longer side) will help us find the required angle??
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22 Dec 2007, 00:34
bmwhype2 wrote:
OA is D.

The angle is dependent on the width.

Why and how? In this case how will you calculate the angle measure?
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Re: Area of a rectangle is 80 What is the angle between the [#permalink]

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07 Nov 2012, 20:33
Another great question from the gmat club...

The theory behind this problem is very simple.
If one can calculate the ratios of the all the sides of a triangle, then one can always always always find the angles.

Let's say that Triangles ABC and DEF are similar.
AB/DE = BC/EF=AC/AF = say 1/2
Draw any triangle satisfying this equation and you will find that
Angle A = Angle D
Angle B = Angle E
Angle C = Angle F

So for the above question, We know the sides of the triangle (diagonal splits the triangle into 2. Additionally we can apply the Pythagoras to calculate the length of the triangle )
So if one were to draw a triangle with sides in the same ratio as that of the triangle(created when we drew the diagonal of the rectangle), then we can always derive the angles !
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Re: Area of a rectangle is 80 What is the angle between the   [#permalink] 07 Nov 2012, 20:33
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# Area of a rectangle is 80 What is the angle between the

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