OK Brilliant People

What is the area of an isosceles trapezoid with diagonals of length 17, all integer side lengths, and a perimeter of 50?

If the diagonals are the same length then it might be a rectangle.

length + breadth =25

\(l^2+b^2=17^2\\ (l+b)^2-2lb=289\\ (25)^2-2lb=289\\ 625-2lb=289\\ -2bl=-336\\ bl=168\)

The area is 168 units squared.     WRONG

I just checked and found that this answer cannot work. It cannot be a rectangle.  

Meoldy: Please look at this picture and see if it is the same. Thanks.

https://www.geogebra.org/m/xqV35GDP

Mmm, your right, Mine is just one possible answer, with regards to the diagonal lengths, and it certainly does not need to be a rectangle. 

Plus I failed to account for the fact that all side lengths are integer.

So in short, mine is wrong.

Did you draw that pic or was it given to you?

I just found it on the Internet.

I have drawn something similar.

The 17 is exact but the 50 is not. 

I drew it in Geobebra and it has variables on a slider so the shape can be changed.

I actually do not think it should be that difficult to answer properly but I have not been sucessful

https://www.geogebra.org/classic/v4uveaev

I see you CPhill answering this question:

Let us see if you agree with I got!!.

Longer side (a):    21

Shorter side (b):   9

Legs (c):                10

Diagonal (d):       17

Height (h)             8

Central mediam:   15

Circumcircle radius (rc): 10.625

Overlap (g):               6

Perimeter (p):           50

Area (A):                    120

Acute angle (α):       53.13

Obtuse angle (β):    126.87

Thanks guest.

Here is the pic.

Did you get some program to work that out?

Here is the link to the actual geogebra build.    https://www.geogebra.org/classic/v4uveaev

Thanks Melody. I most certainly did by using this very nice calculator that solves "trapezoids":

https://rechneronline.de/pi/isosceles-trapezoid.php