Finding the width of a TV Screen

Explanation

The size of a television screen is the diagonal measure of its rectangular screen.  To find the length of a 27-inch screen that is 17 inches high, we use the Pythagorean theorem with \( c \) = 27 and \( b \) = 17

\( c^2 = a^2 + b^2 \)

\( 27^2 = a^2 + 17^2 \)

\( 27^2 - 17^2 = a^2 \)

Since the variable \( a \) represents the length of the television screen, it must be positive.  To find \( a \), we find the positive square root of the result when 17² is subtracted from 27².

Using a radical symbol to indicate this, we have

\[ \sqrt{27^2 - 17^2} = a \]

\[ a = 20.97617696 \approx 21 \]

To the nearest inch, the length of the television screen is 21 inches.