Respuesta :
Pythagoras's theorem provides a simplification of thee relationship between the sides of a right triangle
- The length of the screen is 8 cm
- The width of the screen is 6 cm
Reason:
Known parameters:
Length of the diagonal of the television picture, d = 10 cm
Television screen viewing area, A = 48 cm²
Required:
To find the length and width of the screen
Solution:
Let, L, represent the length of the screen, and let W represent the width of the screen
Considering the right triangle formed by the length, L, the width, W, and a line along the diagonal, d, according to Pythagoras's theorem, we have;
d² = L² + W²
The equation for the area of the screen is A = L × W
Plugging in the known values into the two equations above gives;
10² = L² + W²...(1)
48 = L × W...(2)
From equation (2), we have;
[tex]W = \dfrac{48}{L}[/tex]...(3)
By substituting the expression for W in equation (3) above into equation (1) gives;
[tex]10^2 = \left(\dfrac{48}{L} \right)^2 + L^2 = \dfrac{48^2}{L^2} + L^2[/tex]
10²·L² = 48² + L²⁺² = 48² + (L²)²
Let X represent L², we get;
X = L²
10²·X = 48² + X²
X² - 10²·X + 48² = 0
(X - 64)·(X - 36) = 0
∴ X = L² = 64 or 36
- L = √64 = 8, or L = √36 = 6
The longest side is the length, therefore, the length of the screen, L = 8 cm
From [tex]W = \dfrac{48}{L}[/tex], and L = 8, we have;
- [tex]W = \dfrac{48}{8} = 6[/tex].
The width of the screen, W = 6 cm
Learn more about Pythagoras's theorem here:
https://brainly.com/question/14709662
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