The aspect ratio 16:9 indicates the next relation between x and y:
[tex]\frac{y}{x}=\frac{16}{9}[/tex]
Applying the Pythagorean theorem to the right triangle formed:
[tex]51^2=x^2+y^2[/tex]
Isolating y from the first equation:
[tex]y=\frac{16}{9}x[/tex]
Substituting in the second equation:
[tex]\begin{gathered} 51^2=x^2+(\frac{16}{9}x)^2 \\ 2601=x^2+(\frac{16}{9})^2x^2 \\ 2601=x^2+\frac{16^2}{9^2}^{}x^2 \\ 2601=x^2+\frac{256}{81}^{}x^2 \\ 2601=\frac{337}{81}^{}x^2 \\ 2601\cdot\frac{81}{337}=x^2 \\ 625.166172=x^2 \\ \sqrt[]{625.17}\approx x \\ 25\approx x \end{gathered}[/tex]
Replacing in the equation of y:
[tex]\begin{gathered} y=\frac{16}{9}\cdot25 \\ y\approx44.44 \end{gathered}[/tex]
The approximate dimensions are:
length = 25 in
height = 44.44 in
