A quadrilateral has sides 2,3,9....diagonals are at rt.angles.
Find all possible values of the 4th side....
1wat i did to solve this question during the test was.....i divided the 2 diagonal into two parts each-lets say a a' b and b'
the then formed equations with pythagoras theorem.....three equations....compared it with the options to see which options suit the equations...from the equations i saw dat the square of the 4th side must be 5 less then or 5 more than 81.....so hence ticked root 76 and root 86....maybe my approach is not mathematically correct but it worked for me......
1hey..nishant bhaiya..its Avinav Prakash 4m Heritage....wat ive is that ...taken just x as the lone variable...n used pytha..3 small steps and 2 diff cases..and ans was √76 and √86.....
62guys this one is not that calculation intensive...
Just revisit what i have written in #3.
Or else i will show you what can be done.
11Yup ronald, I know dat, but still I feel raja is r8.
As it is u have it not short enuf after eleminating those 4 variables - now to do it again with a new set of sides is worse than horrible....
Moreover Nishant bhaiya's method might make it shorter.
11@ raja : this is fiitjee aits,,karna padega.
@ avinav : ur probably right.
21array sides change karkey dekho.....thodey aur ans aa jayengey
i mean to say wen sides with length (2 and 9 )are adjacent ....wen (9 and 3) are adjacent and wen (2 and 3) r adjacent
21aur bhi answers they kya?????[11][12]
is this a fiitjee aits q?
11Obviously it was, but what abt the other answers?
Like √56 and √86 ?
21ok i think i got it......teh diagonals of the quadrilateral divide teh quadrilateral into 4 right angle traingles
so from pythagoras theo.
t2+u2=4....................i
w2+v2=81.................ii
u2+v2=9....................iii
i +ii - iii
we get
t2+w2=4+81-9=76
t2+w2=x2=76
x=√76
Wasnt it easy [3]
1array bhaiya is hint sey kuch kaam nai aaya :P...
that thing was in my mind......how to proceed after that ??
62Think of this one geometrically.
First show (convince yourself) that 2 and 3 have to be the adjacent sides...
Then geometrically see how much you can slide the 2 sides 2 and 3 along the diagonal....
I hope this hint gives you a starting point [1]