[tex] a^{2} + b^{2} = c^{2}
[/tex]
Given that c = 40
[tex] c^{2} = 40^{2} [/tex]
[tex] c^{2} = 1600 [/tex]
Let x be the factor
[tex] (16x)^{2} + (9x)^{2} = 1600 [/tex]
[tex] 256x^{2} + 81x^{2} = 1600 [/tex]
[tex] 337x^{2} = 1600 [/tex]
[tex] x^{2} = 1600 / 337[/tex]
[tex] x^{2} = 4.7478[/tex]
[tex]x = \sqrt{4.7478} [/tex]
[tex]x = 2.179 [/tex]
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
