To determine the width of a screen when the height and the aspect ratio are known, follow these steps:
1. Start with the given height of the screen, which is [tex]\(36\)[/tex] cm.
2. Note the aspect ratio of the screen, which is given as [tex]\(4:3\)[/tex]. This means that for every 4 units of width, there are 3 units of height.
3. To find the width, we can use the proportion between the width and height. Set up the proportion by equating the ratio of width to height to the given aspect ratio [tex]\(4:3\)[/tex].
Thus, we have the ratio:
[tex]\[
\frac{\text{width}}{\text{height}} = \frac{4}{3}
\][/tex]
4. Substitute the given height into the proportion:
[tex]\[
\frac{\text{width}}{36} = \frac{4}{3}
\][/tex]
5. To solve for the width, cross-multiply to get:
[tex]\[
3 \times \text{width} = 4 \times 36
\][/tex]
6. Calculate the right side:
[tex]\[
4 \times 36 = 144
\][/tex]
7. Divide by 3 to isolate the width:
[tex]\[
\text{width} = \frac{144}{3}
\][/tex]
8. Perform the division:
[tex]\[
\text{width} = 48
\][/tex]
Therefore, the width of the screen is [tex]\(48\)[/tex] cm.
