ashhad Posted December 1, 2003 Share Posted December 1, 2003 hello, can anyone tell me that if a parallelogram has sides 12 and 2(5)^1/2 and has a height of 4 then what will be the length of the diagonal of that llgm? (ans is 2 (29)^1/2 but how can anyone explain ?) I know , I am missing some basics :shy: Quote Link to comment Share on other sites More sharing options...
vknittala Posted December 1, 2003 Share Posted December 1, 2003 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 Quote Link to comment Share on other sites More sharing options...
lenz Posted December 1, 2003 Share Posted December 1, 2003 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 Quote Link to comment Share on other sites More sharing options...
lenz Posted December 2, 2003 Share Posted December 2, 2003 also, vknittala I'm not sure about the formula you mentioned, length of two diagonals of the parallelogram is different so for which diagonal the formula is applicable :shy: Quote Link to comment Share on other sites More sharing options...
vknittala Posted December 2, 2003 Share Posted December 2, 2003 Hi Lenz, How did you get that AD = BC = 10, and also I am feeling that the two lengths of the diagonals of llgm are same. The formula I gave really works, but I am surprised why is not working here. May be I am wrong, please help me. Thanks Quote Link to comment Share on other sites More sharing options...
lenz Posted December 2, 2003 Share Posted December 2, 2003 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 ? Quote Link to comment Share on other sites More sharing options...
vknittala Posted December 2, 2003 Share Posted December 2, 2003 Hey Lenz, I got your point that two opposites are equal but my question is how did you get 10? Thanks Quote Link to comment Share on other sites More sharing options...
lenz Posted December 2, 2003 Share Posted December 2, 2003 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 Quote Link to comment Share on other sites More sharing options...
sujayath Posted December 2, 2003 Share Posted December 2, 2003 Lenz is correct in his answer. vknittala, You are confusing the formula. The formula you gave for a diagonal is for a box ( or cuboid) and not for a two-dimensional parallelogram. Quote Link to comment Share on other sites More sharing options...
ashhad Posted December 2, 2003 Author Share Posted December 2, 2003 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. Quote Link to comment Share on other sites More sharing options...
vknittala Posted December 2, 2003 Share Posted December 2, 2003 Lenz I got it, I made real simle problem very complicated:)!!! Ok now, the length of the shorter diagonal is 2(29)^1/2 and longer diagonal is 2(53)^1/2 Thanks!!! Quote Link to comment Share on other sites More sharing options...
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