Geometry

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

8/x = x/5

x^2 = 40

x = sqrt 40

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

\(64+x^2+25+x^2=169\)

\(2x^2=80\)

\(x^2=40\)

\(x=2\sqrt{10}\)

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8/x=x/5 (similar triangles)

x^2=40

x=sqrt40=2sqrt10