The height of the outer isosceles triagle is 6.
The inscribed right triangle is 30-60-90 degree, so the sides are x (the hypotenuce), x/2 (the shorter leg), sqrt(3)*x/2 (the longer leg).
The area of the outer triangle is 16*6/2 . It is also 10*(sqrt(3)*x/2)/2=5*sqrt(3)x.
So x=16*6/(5*sqrt(3)) = 96*sqrt(3)/15 = 11.09.