Question

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

Answer 1

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