Answer:
The area of the screen is 1399.68 in²
Step-by-step explanation:
The given parameters are;
The size of the TV = 54 inch
The aspect ratio of the TV screen = 4:3
The size of the TV is given as the length, of the diagonal, therefore, we have;
The aspect ratio = Length, L:Width, W = 4/3 = L/W
L² + W² = 54²..................(1)
L/W = 4/3.........................(2)
Therefore, 3×L = 4×W
L = 4×W/3
Substituting the value of L in equation (1), we have;
(4×W/3)² + W² = 54²
16/9×W² + W² = 54²
25/9×W² = 54²
W² = 54²×9/25 = 1049.76
W = 32.4 inches
The length, L = 4×W/3 = 4×32.4/3 = 216/5 inches = 43.2 inches
The area of the screen = 43.2 inches × 32.4 inches = 1399.68 in²
The area of the screen = 1399.68 in².
