My television set has a screen that is 45 inches high by 60 inches wide and sits on a cabinet that is 45 inches high and 114 inches wide; I have no more space available in the apartment. I like movies and my old TV has an aspect ratio* of 4:3, which makes it impossible to fully see the scenes; a 16:9 aspect ratio SmartTV would be ideal for watching my movies. Here I am, in the store, thinking about buying it; however, only the height is listed in the specifications, which is exactly 45 inches. *In case you don't remember, the aspect ratio is the ratio between the height and width of an image. What is the width of the new SmartTV?

To find the width of the new SmartTV with a height of 45 inches, we can use the aspect ratio to determine the corresponding width. The aspect ratio is defined as the ratio between the height and width of an image. In this case, the desired aspect ratio is 16:9. Let's set up a proportion using the aspect ratios: $$\frac{45}{x} = \frac{16}{9}$$ Cross-multiplying the proportion: $$9 \times 45 = 16 \times x$$ $$405 = 16x$$ Dividing both sides by 16: $$\frac{405}{16} = x$$ $$25.3125= x$$ Therefore, the width of the new SmartTV is approximately 25.3125 inches when the height is 45 inches.