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
$(16x)^{2} + (9x)^{2} = 1600$
$256x^{2} + 81x^{2} = 1600$
$337x^{2} = 1600$
$x^{2} = 1600 / 337$
$x^{2} = 4.7478$
$x = \sqrt{4.7478}$
$x = 2.179$

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