Jump to content
Urch Forums

formula for the finding the diagonal of the parallelogram.


ashhad

Recommended Posts

I have got the answer 2(45)^1/2 using the formulae (l^2 + b^2 + h^2)^1/2.

One more hint:

If you observe one side is 12 and the answer given in the problem is 2 (29)^1/2 which is highly impossible because the length of the doagonal has to be more than the side given.

hope this makes sense :)

Thanks

Link to comment
Share on other sites

I'll try to explain without diagram.

 

Let ABCD be the parallelogram such that AB and CD = 2(5)^1/2 and AD and BC = 10

 

Now draw an altitude BP from the vertex B to the side AD. Since BP forms right angle with the side, you can find AP = sqrt(20-16) = 2

 

Now subtract 2 from total length of AD which is now equal to 10

 

Now the hypeteneous BD which is also a diagonal = SQRT( 100 + 16) = sqrt(116) = 2 (29)^1/2

 

Please note that length of the two diagonals are different for a parallelogram. So you have to refer to the diagram or other additional information to know length which diagonal is required and solve it

 

 

 

 

Link to comment
Share on other sites

Hi vknittala,

 

Parellelogram property says that opposite sides are equal. Since AD and BC are opposite side, they are equal.

 

I just saw all the properties of the parellelogram in the book, no where it says two diagonals are equal in length. Also, it makes sense to me.

 

And the formula that you are talking about may not be true for parellelogram.....not sure..just check once again from where you picked up ?

 

 

Link to comment
Share on other sites

ok..ok..I got it what you are saying....go through all the steps I mentioned in the first reply line by line.....I got 2 by applying pythgorian theorem to 4^2 - (2(5)^1/2 )^2 which gives me ans as 2...and this is a part of the length(AP) of one of the sides AD. And PB = AD - AP = 12-2 = 10 and this is perpendicular to heights 4 and the hypotenus is formed by the diagonal which we want...and there fore...10^2 + 4^2 = 116. and sqrt of this is the answer..

 

Hope this clears your doubt. If you are still not clear, let me know...:D

Link to comment
Share on other sites

hello guls ang guys,

the

after a long debate the enigma has solved, I know why vknittala has confused , because in the first reply of lenz, lenz had mistakenly taken BC and AD =10 but in the original post it is 12 instead of 10.

Thanks lenz for your solution.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...