Aspect ratio of a rectangular TV

[rafael.quigod]

The question is:

The "aspect ratio" of a rectangular TV screen is the ratio of its width to its height.

Quantity A = the area of a rectangular TB screen with an aspect ratio of 4:3 and a diagonal of 25

Quant B= the area of a rectangular TV screen with an aspect ratio 16:9 and a diagonal of 25

My doubt is why does the author concludes that width (for QA) is 4x and height is 3x. In concrete, why suddenly the x (as variable) appears? Why not just use 4 as width and 3 as lenght, without adding the variable?

Best regards

Rafael

[tommywallach]

Hey Rafael,

This is a way of expressing ratios that is often used for more complex ratio questions. It's called "the unknown multiplier." Basically, if you know the ratio of something is 3 to 4, you can always call it 3x and 4x, because it could be 3 and 4 (meaning x = 1) or 6 and 8 (meaning x = 2) or 9 and 12 (meaning x = 3), and on and on.

You're also welcome to plug in numbers, but sometimes the x can be helpful in solving more quickly. For example:

A class of students has boys and girls in a ratio of 4 to 5. If two boys leave and one girl joins the class, the ratio will be 2 to 3. How many boys were in the class to begin with?

This question is easiest solved by calling the boys 4x and the girls 5x. Then you only need one equation to solve:

(4x - 2) / (5x + 1) = 2/3

Hope that helps!

-t