Question

Ava has a large-screen TV. The TV has a screen with a 51-inch diagonal and a width of 45 inches. The base of the TV is 4 inches from the bottom of the screen. What is the total height, h, in inches of the TV?

Answer 1

To find the total height of the TV, we can start with the information provided: the diagonal of the screen is 51 inches and the width is 45 inches. We will use the Pythagorean theorem to find the height of the screen itself.

First, denote:
- Diagonal of the screen \( d = 51 \) inches
- Width of the screen \( w = 45 \) inches
- Height of the screen \( h_s \) (we need to find this)

According to the Pythagorean theorem:

\[
d^2 = w^2 + h_s^2
\]

Substituting the values we have:

\[
51^2 = 45^2 + h_s^2
\]

Calculating the squares:

\[
2601 = 2025 + h_s^2
\]

Now, subtract \( 2025 \) from both sides:

\[
h_s^2 = 2601 - 2025
\]
\[
h_s^2 = 576
\]

Taking the square root of both sides gives:

\[
h_s = \sqrt{576} = 24 \text{ inches}
\]

Now, to find the total height \( h \) of the TV, we need to add the height of the screen to the height of the base:

- Height of the base of the TV \( b = 4 \) inches

Thus, the total height \( h \) is:

\[
h = h_s + b = 24 + 4 = 28 \text{ inches}
\]

So, the total height of the TV is:

\[
\boxed{28} \text{ inches}
\]