Question

The size of a TV is the diagonal length of the TV. Use a Pythagorean triple to find the length of a 20-inch TV, given that its width is 12 inches.(1 point)

Answer 1

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.