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jabs
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 May 2003, 04:56
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what is the length of the other diagonal?


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A parallelogram has 2 sides as14, 18 one of the diagonals is 16, what is the length of the othe diagonal? Working appreciated.Thanks!!
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arun
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 May 2003, 13:05
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answer: 24

explanation: calculate area of the triangle with sides 16,14,18 using hercules formula ie (area)^2=s(s-a)(s-b)(s-c) where s=(a+b+c)/2
so area=96.

this area=1/2*16*h (h is altitude- diagonals bisect each other, 16 base which is bisected by the altitude)
therefore h=12

other diagonal=2h=24
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stolyar
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 10 May 2003, 07:06
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another feature to remember:

for a parallelogram --- d1^2+d2^2=2*[a^2+b^2]

the sum of squares of diagonals equals to two sums of squares of sides.
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gmatblast
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 28 Feb 2004, 18:38
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(d1^2 + d2^2) = 2(l1^2 + l2^2)

Substitute d1 = 16, l1 = 18, l2 = 14

d2 = 28 (answer)
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gayathri
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 Nov 2004, 20:46
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Is the answer 28?

I used the formula d1^2 + d2^2 =2(a^2+b^2)

where d1 and d2 are the two diagonals and a and b are the two sides.

Is this a GMAT question?
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Paul
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 09 Nov 2004, 21:30
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OA is 28
Nice gayathri. I just wanted to bring up this formula as it could be useful. You just never know, the GMAT is full of surprises.
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MA
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what Updated on: 01 May 2005, 17:57
Originally posted by MA on 01 May 2005, 15:04.
Last edited by MA on 01 May 2005, 17:57, edited 3 times in total.
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Paul
a parallelogram has 2 sides:14, 18 one of the diagonals is 16, what is the length of the othe diagonal?
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it is useful concept to all. therefore, i thought it is useful to bring it into the discussion.

Sum of the square of Diagnals of parallogram = D1^2 + D2^2 = 2 (a^2 + b^2), Where D1 and D2 are the two diagonals and a and b are the two different sides of the parallogram.
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GMATT73
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 24 Sep 2005, 16:56
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Length of the second diagnol is 44.

Area(parallelogram)=18X14=252/2=176 (Area of each triangle)

Base/2Xheight=Area(triangles)

16/2XH=176

H=22

22X2=44
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Natalya Khimich
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 25 Sep 2005, 21:30
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It's a very good question.
lets a and b - sides
d1 and d2 diagonals
The key formular is:
d1^2+d2^2=2*(a^2+b^2).

from that another digonal is 28 ( if I'm not mistaken in calculations).
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richardj
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 27 Sep 2005, 07:42
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Difficult to describe.

Draw a big rectangle on a sheet of paper.
Its height is y.
Its length is 18+x.
On the top mark x from the left.
On the bottom mark x from the right.
Draw in the parallelogram inscribed within this rectangle.
(By drawing line from bottom left corner to point on top x from left.)
Mark a rectangle on the left, which is x wide, y high.
The diagonal is 14. Side of parallelogram.

So x^2 + y^2 = 14^2 = 196 (E1)

Let z = 18 - x (E2), z is the middle width portion of the rectangle.

Then you can split the bottom line, into three parts,
x, z, x.
Now we know the length of the shorter diagonal 16.
But this is the hypotenuse of a triangle.
The sides are y and z.

So y^2 + z^2 = 16^2 = 256 (E3)

(E3) - (E1)
z^2 - x^2 = 60
From (E2) z = 18 - x
So z^2 = 18^2 - 36x + x^2

(324 - 36x + x^2) - x^2 = 60
(324 - 60) = 36x
x = 264 / 36 = 22 / 3

Hence (E2)
z = 18 - 22/3 = 32/3

And (E1)
y^2 = 196 - x^2 = 196 - (22/3)^2
y^2 = (1764 - 484) / 9 = 1280/9

Width of rectangle,
w = 18 + x = (54+22)/3 = 76/3

Diagonal d
d^2 = w^2 + y^2
d^2 = (76^2)/9 + 1280/9
d^2 = (5776+1280)/9 = 7056/9
d = 84/3 = 28

But there would not be time to do this in the real GMAT.
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A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 27 Sep 2005, 15:06
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vikramm
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d1^2+d2^2=2*(a^2+b^2).
I'm not sure if that formula applies to a parallelogram. Looks more like what would apply to a kite (adjacent sides equal and diagonals perpendicular).

Couldn't find this anywhere through google. Does anyone have a link?
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I too was wondering where from this new formula came. A little trignometry helped derive formula though. Anyone interested in derivation can look into attached doc.

For others, get this formula in your kitty.
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parallelogram_diagonal_formula.doc [25 KiB]
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