TV screens are measured by their diagonals. If the diagonal of a TV screen is 30 inches, and the ratio of the height to the width is 3:5, what are the height and width of the screen? (Round each to hundredth of an inch).

The two screen dimensions are 15.43 inches and 25.72 inches.

Step-by-step explanation:

Ratio is 3:5, or

     3

      5

Now multiply both numerator and denominator by the constant k:

   3k

  5k

Note that 3k and 5k represent the actual screen dimensions, in inches.

Applying the Pythagorean Theorem, we get:

(3k)^2 + (5k)^2 = 30^2     (since 30 is the length of the diagonal)

Then 9k^2 + 25 k^2 = 900, and

            k^2(9 + 25) = 900, or

             k^2 = 900/34 = 26.47

             Then k = +√26.47 = 5.145

This k is the constant of proportionality.

The width of the screen is 3k, which here is 15.43 inches, and the length is 5k, which here is 25.72 inches.

The two screen dimensions are 15.43 inches and 25.72 inches.

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