Question

James brought a 55" TV. If its aspect ratio is 4:3 what is its areaChoices:A. 3025in squaredB. 1452in squaredC. 33in squareD. 121in squared

Answer 1

We have the following:

55 inches indicates the diagonal of the TV, therefore:

let x a side A

let y a side B

`\begin{gathered} 3x=4y \\ x=(4)/(3)y \end{gathered}`

now, with the Pythagorean theorem

`\begin{gathered} 55^2=x^2+y^2 \\ 3025=((4)/(3)y)^2+y^2 \\ 3025=(16)/(9)y^2+y^2 \\ (25)/(9)y^2=3025 \\ y=\sqrt[]{3025\cdot(9)/(25)} \\ y=\sqrt[]{1089} \\ y=33 \end{gathered}`

for x:

`\begin{gathered} x=(4)/(3)\cdot33 \\ x=44 \end{gathered}`

Side A= 44 in

Side B = 33 in

The area:

`a=A\cdot B=44\cdot33=1452`

The answer is 1452 inches squared, the option B