Question

The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in a 4:3 format, meaning the ratio of the length to width of the screen is 4 to 3.

What is the area of a 41 inch traditional TV screen? What is the area of a 41 inch LCD TV whose screen is in a 16:9 format? Which screen is larger?

Answer 1

41inch traditional tv means the diagonal is of length 41 inches and length : breadth = 4:3
Let length = 4x and breadth = 3x
Applying pythagoreaon theorem we get
(4x)² + (3x)² = 41²
(5x)² = 41²
5x = (41)
X= (41)/5

Area of traditional TV = length * breadth = 4(41)/5 * 3 (41)/5 = 12 * 41² / 25 = 806.88 sq inches

41inch LCD tv means the diagonal is of length 41 inches and length : breadth = 16:9
Let length = 16x and breadth = 9x
Applying pythagoreaon theorem we get
(16x)² + (9x)² = 41²
(337^0.5 x)² = 41²
337^0.5 x = (41)
x= (41)/337^1/2

Area of LCD TV = length * breadth = 16(41)/337^1/2 * 9 (41)/337^1/2 = 12 * 41² / 25 = 718.29 sq inches

As we can see, the traditional screen is larger

NOTE: The squarer the TV is, the larger will be its area for the same length of diagonal