Question

a small television has a picture with a diagonal measure 10 cm and a viewing area of 48 cm^2. Find the length and width of the screen

Answer 1

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;

$W = \dfrac{48}{L}$...(3)

By substituting the expression for W in equation (3) above into equation (1) gives;

$10^2 = \left(\dfrac{48}{L} \right)^2 + L^2 = \dfrac{48^2}{L^2} + L^2$

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 $W = \dfrac{48}{L}$, and L = 8, we have;

• $W = \dfrac{48}{8} = 6$.

The width of the screen, W = 6 cm

Learn more about Pythagoras's theorem here:

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