the ratio of the width to height of an HDTV screen is 16 to 9 and for an older traditional screen is 4 to 3. for a 60.0 in. screen of each type, which is the greater area, and by what by percent
and the answer is traditional screen area is 12% more than HDTV screen
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See diagram.
TV size = diagonal = D
Aspect ratio R = Width W/height H
R² = W²/H² and W = HR
D² = W² + H² = H² ( R²+1)
Thus we get H = D / √(R²+1) W = H R = DR /√(R²+1)
Area = W H = H² R = D²R / (R²+1)
For HDTV : R = 16/9 D = 60 inches
Area = 60² 16 / [ 9 * (16²/9² + 1) ] = 1538 inch²
For Traditional TV : R = 4/3 D = 60"
Area = 1728 in² This is 12.3 % more than HDTV
TV size = diagonal = D
Aspect ratio R = Width W/height H
R² = W²/H² and W = HR
D² = W² + H² = H² ( R²+1)
Thus we get H = D / √(R²+1) W = H R = DR /√(R²+1)
Area = W H = H² R = D²R / (R²+1)
For HDTV : R = 16/9 D = 60 inches
Area = 60² 16 / [ 9 * (16²/9² + 1) ] = 1538 inch²
For Traditional TV : R = 4/3 D = 60"
Area = 1728 in² This is 12.3 % more than HDTV
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kvnmurty:
thanks & u r welcome.
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