Math CentralQuandaries & Queries


The ratio of height to width for a tv screen is 9 to 16. How high is a screen that is 30 in. wide?
I don't know how to work this, we have to show our work.

Hi Katie,

We are not quite sure we understand your question.

Since the ratio of the height to the width is 9 to 16 then the screen is 9x inches high and 16x inches wide for some number x. If the screen is truly 30" WIDE, we can say

30" = 16x

Solve for x, and then use this to find the height of the screen (9x).

Usually however the "size" of a TV screen is the length of the diagonal. Hence if this is a "30 inch TV" then the diagonal is 30 inches long.

If this is the case, draw a right-triangle and label the hypotenuse as 30".

Label the height as 9x, and the width as 16x.

Now you can use Pythagoras' theorem to solve for x.

Hope that helps.

Gabriel and Penny

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