Question

Television screens are described by their diagonal measurement and by their length to width ratio many widescreen televisions have a length to width ratio of 16:9 if you have a 40 inch.widescreen television with an aspect ratio of 16:9 could you fit it in a piece of furniture with an opening that is 37 inches by 24 inches ?

Answer 1

`a^(2) + b^(2) = c^(2)`
Given that c = 40

`c^(2) = 40^(2)`

`c^(2) = 1600`

Let x be the factor

`(16x)^(2) + (9x)^(2) = 1600`

`256x^(2) + 81x^(2) = 1600`

`337x^(2) = 1600`

`x^(2) = 1600 / 337`

`x^(2) = 4.7478`

`x = √(4.7478)`

`x = 2.179`

Therefore:
16x = 2.179 x 16 = 34.86
9x = 2.179 x 9 = 19.61

The television is approx 34.86 by 19.61 inches. So, yes, it can fit in an opening of 37 by 24 inches