Geometry

8 is to x   as x is to 5   (similar triangles)

8/x = x/5

x^2 = 40

x = sqrt 40

$(\sqrt{8^2+x^2})^2+(\sqrt{5^2+x^2})^2=(5+8)^2$

$64+x^2+25+x^2=169$

$2x^2=80$

$x^2=40$

$x=2\sqrt{10}$

8/x=x/5 (similar triangles)

x^2=40

x=sqrt40=2sqrt10