Question

Find the width of a newer 48-in TV whose screen has an aspect ratio of 16:9what is the width?

Answer 1

Answer:

The width of the TV is 41.84-in

Explanations:

The diagonal size of the TV, d= 48 in

The aspect ratio= 16 : 9

The aspect ratio is usually given in form of width : Height

Let the width = w

Let the height = h

The diagram looks like:

`\begin{gathered} (w)/(h)=\text{ }(16)/(9) \\ h\text{ = }(9w)/(16) \end{gathered}`

Using the Pythagoras theorem:

`\begin{gathered} d^2=h^2+w^2 \\ 48^2\text{ = (}(9w)/(16))^2+w^2 \\ 2304\text{ = }(81w^2)/(256)+w^2 \\ \text{Multiply through by 256} \\ 589824=81w^2+256w^2 \\ 589824\text{ = }337w^2 \\ w^2\text{ = }(589824)/(337) \\ w^2\text{ = 1750.22} \\ w\text{ = }\sqrt[]{1750.22} \\ w\text{ = 41.84 } \end{gathered}`

The width of the TV is 41.84-in