Question

Calculate the width of a 70" TV if the TV has an aspect ratio of 16:9.

Answer 1

The TV has a length of 61.01" and a height of 34.32"

Explanation:

The size of a TV is given by the length of it's diagonal, in this case the diagonal of the TV is 70". The ratio of the screen is 16:9, which means that for every 16 units on the length of the tv there are 9 inches on its height. The diagonal of the screen forms a right angle with the length and the width, therefore we can apply Pythagora's theorem as shown below:

`diagonal^2 = height^2 + length^2\\\\height^2 + length^2 = (70)^2\\\\height^2 + length^2 = 4900`

Since the ratio is 16:9, we have:

`9*length = 16*height`

`length = (16)/(9)*height`

Applying this on the first equation, we have:

`height^2 + ((16)/(9)*height)^2 = 4900\\\\height^2 + (256)/(81)*height^2 = 4900\\\\(337)/(81)*height^2 = 4900\\\\height^2 = (4900*81)/(337)\\\\height^2 = (396900)/(337)\\\\height^2 = 1177.744\\\\height = √(1177.744)\\\\height = 34.32`

`length = (16)/(9)*34.32\\\\length = 61.01`

The TV has a length of 61.01" and a height of 34.32"