Answer
See below.
Work Step by Step
Using the Pythagorean Theorem and the fact that $x$ is non-negative we get: $(9x)^2+(16x)^2=32^2\\81x^2+256x^2=1024\\337x^2=1024\\x^2=\frac{1024}{337}\\x=\sqrt{\frac{1024}{337}}$
Hence the height: $9x=9\sqrt{\frac{1024}{337}}\approx15.69$ in and the width is: $16x=16\sqrt{\frac{1024}{337}}\approx27.89$ in
