To find the length of a 20-inch TV with a width of 12 inches, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the lengths of the two shorter sides (width and height) of the TV, and \(c\) is the diagonal (size of the TV).
Here, we have:
- \(c = 20\) inches (the diagonal)
- \(a = 12\) inches (the width)
We need to find \(b\) (the height). Substituting the known values into the Pythagorean theorem:
\[ 12^2 + b^2 = 20^2 \]
Calculating the squares:
\[ 144 + b^2 = 400 \]
Now, subtracting \(144\) from both sides:
\[ b^2 = 400 - 144 \] \[ b^2 = 256 \]
Taking the square root of both sides to find \(b\):
\[ b = \sqrt{256} = 16 \]
Thus, the height of the TV is \(16\) inches. Therefore, the dimensions of the TV are:
- Width: 12 inches
- Height: 16 inches
- Diagonal: 20 inches.