jmc

The area of the two squares are $(2x{)}^2=4x^2$ square inches and $(5x{)}^2=25x^2$ square inches, and the area of the triangle is $\frac{1}{2}(2x)(5x)=5x^2$ square inches. We solve $$25x^2+4x^2+5x^2=850$$ to find $x=\pm \sqrt{850/34}=\pm 5$. We take the positive solution $x=\boxed{5}$.