The Traditional TVs is larger than LCD tv screen
What is diagonal of rectangle?
The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices.
The length of diagonals of a rectangle can be calculated as:
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
According to the question
The screen size of a television is determined by the length of the diagonal of the rectangular screen.
Traditional TVs
Ratio of the length to width = 4:3
Let a be the constant for both length and width
therefore
Length of Traditional TVs = 4a
Width of Traditional TVs = 3a
The area of a 27-inch traditional tv screen
i.e
Diagonal of Traditional TVs = 27
Now applying formula of diagonal of rectangle
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
substituting the values
27 = [tex]\sqrt{(4a)^{2} + (3a)^{2} }[/tex]
27 = [tex]\sqrt{16a^{2} + 9a^{2} }[/tex]
27 = [tex]\sqrt{25a^{2} }[/tex]
27 = ± 5a
a cannot be -ve
a = 5.4
now,
Length of Traditional TVs = 4* 5.4 = 21.6 inches
Width of Traditional TVs = 3 * 5.4 = 16.2 inches
Area of Traditional TVs = Length * width
= 21.6 * 16.2
= 349.92 [tex]inches^{2}[/tex]
LCD TVs
Ratio of the length to width = 16:9
Let a be the constant for both length and width
therefore
Length of LCD TVs = 16a
Width of LCD TVs = 9a
The area of a 27-inch LCD TVs screen
i.e
Diagonal of LCD TVs= 27
Now applying formula of diagonal of rectangle
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
substituting the values
27 = [tex]\sqrt{(16a)^{2} + (9a)^{2} }[/tex]
27 = [tex]\sqrt{256a^{2} + 81a^{2} }[/tex]
27 = [tex]\sqrt{337a^{2} }[/tex]
27 = ± 18.357a
a cannot be -ve
a = 1.47
now,
Length of LCD TVs = 16*1.47 = 23.53
Width of LCD TVs = 9*1.47 = 13.23
Area of Traditional TVs = Length * width
= 21.6 * 16.2
= 311.30 [tex]inches^{2}[/tex]
Hence, the Traditional TVs is larger than LCD tv screen .
To know more about diagonal of rectangle here:
https://brainly.com/question/26044249
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