Sandy purchases an entertainment center that has an opening measuring 42 inches by 20.5 inches. If widescreen televisions (16.9 aspect ratio) are on sale at the local electronics center, what is the maximum screen size that Sandy should purchase, assuming that each screen has a 1 inch wide frame bordering the screen?
Thank you much in advance!
width: 40 inches. height=40*9/16
(2 + x) > 20.5
(2 + (16/9)x) <42
x < 18.5
x < 22.5
To determine the maximum screen size that Sandy should purchase, we need to consider the dimensions of the opening and take into account the aspect ratio of 16:9 and the 1 inch wide frame bordering the screen.
First, let's calculate the maximum height of the screen. We know that the width of the opening is 42 inches. Since the aspect ratio of widescreen televisions is 16:9, the height can be calculated by dividing the width by 16 and then multiplying by 9:
Max Height = (Width / 16) * 9
= (42 / 16) * 9
≈ 23.625 inches
Next, we need to reduce the height of the screen by accounting for the 1 inch wide frame bordering the screen. Subtracting this from the height:
Effective Height = Max Height - 2 * Frame Width
= 23.625 - 2 * 1
≈ 21.625 inches
Therefore, the maximum screen size Sandy should purchase would have a width of 42 inches and a height of approximately 21.625 inches.