Last visit was: 22 Apr 2026, 18:56 It is currently 22 Apr 2026, 18:56
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
jabs
avatar
Joined: 27 Apr 2003
Last visit: 28 Sep 2003
Posts: 31
Own Kudos:
4
 [4]
Posts: 31
Kudos: 4
 [4]
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 May 2003, 04:56
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 4 sessions

History

Date
Time
Result
Not Attempted Yet
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what is the length of the other diagonal?


Show Spoiler
A parallelogram has 2 sides as14, 18 one of the diagonals is 16, what is the length of the othe diagonal? Working appreciated.Thanks!!
User avatar
arun
User avatar
Joined: 07 May 2003
Last visit: 30 Jul 2003
Posts: 10
Own Kudos:
2
 [2]
Posts: 10
Kudos: 2
 [2]
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 May 2003, 13:05
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
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
avatar
stolyar
avatar
Joined: 03 Feb 2003
Last visit: 06 May 2014
Posts: 1,012
Own Kudos:
1,883
Posts: 1,012
Kudos: 1,883
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 10 May 2003, 07:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
gmatblast
User avatar
Joined: 11 Nov 2003
Last visit: 27 Dec 2004
Posts: 190
Own Kudos:
68
Location: Illinois
Posts: 190
Kudos: 68
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 28 Feb 2004, 18:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(d1^2 + d2^2) = 2(l1^2 + l2^2)

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

d2 = 28 (answer)
User avatar
gayathri
User avatar
Joined: 07 Nov 2004
Last visit: 24 Oct 2006
Posts: 364
Own Kudos:
507
 [2]
Posts: 364
Kudos: 507
 [2]
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 08 Nov 2004, 20:46
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
Paul
User avatar
Joined: 15 Dec 2003
Last visit: 10 Nov 2012
Posts: 2,707
Own Kudos:
1,651
Posts: 2,707
Kudos: 1,651
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 09 Nov 2004, 21:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
533
 [1]
Posts: 695
Kudos: 533
 [1]
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.
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Paul
a parallelogram has 2 sides:14, 18 one of the diagonals is 16, what is the length of the othe diagonal?
Show more


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.
User avatar
GMATT73
User avatar
Joined: 29 Jan 2005
Last visit: 28 Dec 2011
Posts: 2,877
Own Kudos:
1,290
Posts: 2,877
Kudos: 1,290
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 24 Sep 2005, 16:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Natalya Khimich
User avatar
Joined: 13 Aug 2005
Last visit: 24 Jan 2007
Posts: 56
Own Kudos:
4
Posts: 56
Kudos: 4
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 25 Sep 2005, 21:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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).
User avatar
richardj
User avatar
Joined: 06 Aug 2005
Last visit: 23 Oct 2005
Posts: 91
Own Kudos:
26
Posts: 91
Kudos: 26
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 27 Sep 2005, 07:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
duttsit
User avatar
Joined: 22 Aug 2005
Last visit: 19 Feb 2016
Posts: 493
Own Kudos:
708
Location: CA
Posts: 493
Kudos: 708
A parallelogram has 2 sides: 14, 18 one of the diagonals is 16, what 27 Sep 2005, 15:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vikramm
Quote:
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?
Show more

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.
Attachments

parallelogram_diagonal_formula.doc [25 KiB]
Downloaded 622 times

Moderators:
Bunuel
Math Expert
109754 posts
Krunaal
Tuck School Moderator
853 posts