Answer:
a) Width to height is 16:9
Width = 32
32 / 16 = 2
2 * 9 = 18
Size of TV = Length of diagonal (use pythagorean theorem)
Length of diagonal = [tex]\sqrt{Width^{2} + Height^{2} }[/tex] = [tex]\sqrt{32^{2} + 18^{2} }[/tex] = 36.72 (round to the nearest hundredth)
b) Diagonal = 60 and width to height is 16:9
[tex]\sqrt{16^{2} + 9^{2} }[/tex] = [tex]\sqrt{337}[/tex]
16 / [tex]\sqrt{337}[/tex] = 0.87 (round to the nearest hundredth)
Width = 60 * 0.87 = 52.2
52.2 / 16 = 3.26 (round to the nearest hundredth)
Height = 3.26 * 9 = 29.34
Checking: [tex]\sqrt{52.2^{2} + 29.34^{2} }[/tex] = 59.88 (round to the nearest hundredth)
It is close to 60, because of some rounding to the nearest hundredth
