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

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Area of a rectangle is 80 What is the angle between the [#permalink] New post 23 Oct 2007, 12:42
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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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Re: DS - Area of a Rectangle [#permalink] New post 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


Answer D
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Re: DS - Area of a Rectangle [#permalink] New post 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


Answer D


Is there another way to solve this? I dont think TAN, SINE. COSINE are tested on the gmat.
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 [#permalink] New post 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

the answer is (D)

:)
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 [#permalink] New post 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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 [#permalink] New post 20 Dec 2007, 15:05
OA is D.

The angle is dependent on the width.
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 [#permalink] New post 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] New post 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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 [#permalink] New post 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

the answer is (D)

:)


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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 [#permalink] New post 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] New post 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.

You may ask how ?
Well, think about this
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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