Question

You just bought a new 52" wide screen TV online, and this was the only information they gave you (in terms of the size). Fortunately, you took AQR (Algebra, Quantitative Reasoning) and you know that the aspect ratio of this TV is 16:9. To make sure that it will fit in your living room, find the approximate dimensions of the TV.

A) Width: 52 inches, Height: 29.25 inches
B) Width: 48 inches, Height: 27 inches
C) Width: 56 inches, Height: 31.5 inches
D) Width: 60 inches, Height: 33.75 inches

Answer 1

Using the 16:9 aspect ratio and the given width of 52 inches, we determined that the height of the TV is approximately 29.25 inches. Therefore, the correct choice is option A) Width: 52 inches, Height: 29.25 inches.

Step-by-step explanation:

To determine the approximate dimensions of the TV based on a 52" wide screen TV with a 16:9 aspect ratio, we use the ratio to express the dimensions in terms of one another. Since a 16:9 ratio means that for every 16 units of width, there are 9 units of height, we can set up a proportion to find the height when the width is 52 inches.

The ratio representing width to height is 16/9, which can also be written as:

Width/Height = 16/9
Using the given width of 52 inches, we can set up the proportion:

52/Height = 16/9

By cross-multiplying, we get:

9 x 52 = 16 x Height

Height = (9 x 52) / 16

Height ≈ 29.25 inches

Therefore, the approximate dimensions of the TV will be a width of 52 inches and a height of 29.25 inches, which corresponds to option A).