help :(

- imqwerty

help :(

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- schrodinger

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- imqwerty

We have a quadrilateral ABCD with AB+CD+AC=20cm and the area of quadrilateral is 50cm^2. Find the length of diagonal BD.

- Loser66

@phi

- phi

Does this question have a figure ? If so, can you post it or a sketch?

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## More answers

- imqwerty

ok wait

- imqwerty

|dw:1437311000849:dw|

- phi

yes, it will take some musing.

- imqwerty

my math professor gave me this question...he has a hole lot of such amusing questions. :)

- phi

what techniques have you been studying? maybe there is a hint there?

- imqwerty

we've been studying- solutions of triangles
trignometry
sequences nd series

- phi

If I get any bright ideas, I'll post it.

- imqwerty

ok thanks :)

- imqwerty

ok

- danica518

DANG MAN

- danica518

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

- danica518

it has to be the key to getting an expression for some unknowns

- danica518

|dw:1437239446838:dw|

- danica518

uh lets just take some arb values see a possiblity

- danica518

do you think we have to give him like an expression for the solution

- danica518

like this this Z shape for instance

- danica518

we can reshape the Z in many ways and still maintain 50 cm^2 i think there is no problem with that

- danica518

|dw:1437239633806:dw|

- imqwerty

we have to give direct numerical answer nt an expression..thanks fr helping :)

- danica518

|dw:1437239689188:dw|

- danica518

but look at this, this illustration atleast tells us there have to be multiple possiblities

- danica518

if i vary the angles between the lines that form Z, and vary the lengths incolved in eaach segment of the Z

- danica518

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

- danica518

oh maybe it comes down to the possible hypotenuse u can even form with a triangle

- danica518

oh that could be helpful, we should consider the possible legs of a triangle and the maximum area they can produce

- danica518

|dw:1437239899601:dw|

- imqwerty

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.

- danica518

|dw:1437240237972:dw|

- danica518

lets see if we can rewrite the area expression with respect to theta and phi now with the diagonal length changes

- danica518

|dw:1437240322515:dw|

- danica518

what can you saw about the opposite angles wrt to theta and phi?

- danica518

|dw:1437240370715:dw|

- danica518

are there pair of similiar triangles for all quad?

- imqwerty

nt necessary

- imqwerty

they may be similar they may be nt

- danica518

why

- imqwerty

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.

- imqwerty

@Empty

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