Question

only for math genius..
full explanation is needed
I'll mark the correct explanation as brainliest..
for your convenience answer is 15.let's see who is genius here..
un-neccesary ones will be reported..

Answer 1

Consider the diagonal as AB. it interests the 3 unit line at D .
let the angle between AB and 9 unit line is C .
then AB= 9secC + 12secC
9secC×sinC + 12secC×sinC = 3 or
tanC = 1/7 .
$or \: \sec(c) = \frac{5 \sqrt{2} }{7} .$
So AB = (9+12)secC .
$or \: 15 \sqrt{2} \\ now \: we \: know \: lenth \: of \: diagonal \: is \: x \sqrt{2}$
so comparing we get x = 15 .

Answer 2

this is ur required result in attachment