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We have the following:
55 inches indicates the diagonal of the TV, therefore:
let x a side A
let y a side B
[tex]\begin{gathered} 3x=4y \\ x=\frac{4}{3}y \end{gathered}[/tex]now, with the Pythagorean theorem
[tex]\begin{gathered} 55^2=x^2+y^2 \\ 3025=(\frac{4}{3}y)^2+y^2 \\ 3025=\frac{16}{9}y^2+y^2 \\ \frac{25}{9}y^2=3025 \\ y=\sqrt[]{3025\cdot\frac{9}{25}} \\ y=\sqrt[]{1089} \\ y=33 \end{gathered}[/tex]for x:
[tex]\begin{gathered} x=\frac{4}{3}\cdot33 \\ x=44 \end{gathered}[/tex]Side A= 44 in
Side B = 33 in
The area:
[tex]a=A\cdot B=44\cdot33=1452[/tex]The answer is 1452 inches squared, the option B
