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We have a quadrilateral ABCD with AB+CD+AC=20cm and the area of quadrilateral is 50cm^2. Find the length of diagonal BD.
Does this question have a figure ? If so, can you post it or a sketch?
yes, it will take some musing.
my math professor gave me this question...he has a hole lot of such amusing questions. :)
what techniques have you been studying? maybe there is a hint there?
we've been studying- solutions of triangles trignometry sequences nd series
If I get any bright ideas, I'll post it.
ok thanks :)
the length of diagonal as a function of the length of the opposite sides, i feel like there is another variable involved but i think we can write a dependant function of these variables
it has to be the key to getting an expression for some unknowns
uh lets just take some arb values see a possiblity
do you think we have to give him like an expression for the solution
like this this Z shape for instance
we can reshape the Z in many ways and still maintain 50 cm^2 i think there is no problem with that
we have to give direct numerical answer nt an expression..thanks fr helping :)
but look at this, this illustration atleast tells us there have to be multiple possiblities
if i vary the angles between the lines that form Z, and vary the lengths incolved in eaach segment of the Z
i can think of ways the solution might be limited to just 1 answer, if it was asking is there a integer solution or something
oh maybe it comes down to the possible hypotenuse u can even form with a triangle
oh that could be helpful, we should consider the possible legs of a triangle and the maximum area they can produce
u mean that if v change the angles between the lines of z then v can have multiple solutions but v must keep the area in mind it may be possible that the area may change when we change the angles between the lines of z.
lets see if we can rewrite the area expression with respect to theta and phi now with the diagonal length changes
what can you saw about the opposite angles wrt to theta and phi?
are there pair of similiar triangles for all quad?
they may be similar they may be nt
wait.. if any 2 triangles in the quad. r similar then the other 2 must also be similar so the triangle must be a parallelogram nd if it is a paralle.. then the 2 opposite sides r equal nd the diagonal would also be equal. and if u do the calculations taking the case of a parallelogram nd try to find side lengths then the answers would be like negative sides.