The problem is about finding the width $w$ of a computer monitor using its diagonal $d$ and height. The diagram shows the monitor’s diagonal $d = 23$ inches, and the height of the monitor is $16$ inches.

This forms a right triangle where:

• $w$ is the width of the monitor,
• $h = 16$ inches is the height of the monitor, and
• $d = 23$ inches is the diagonal.

Using the Pythagorean theorem for right triangles:

$d^2 = w^2 + h^2$

Substituting the values:

$23^2 = w^2 + 16^2$

Solving for $w$:

$w^2 = 23^2 - 16^2$

$w = \sqrt{23^2 - 16^2}$

Thus, the correct equation to find $w$ is:

$w = \sqrt{23^2 - 16^2}$

The correct answer is the third option: $w = \sqrt{23^2 - 16^2}$

Would you like more detailed calculations or further clarifications?

Here are 5 related questions to expand on this:

1. How would the Pythagorean theorem change if you knew the width and diagonal but not the height?
2. What would the width of the screen be if the diagonal was changed to 25 inches and the height remained the same?
3. How can this concept be applied to other real-world applications involving diagonal measurements?
4. Can you use trigonometry (such as sine or cosine) to find the angle between the diagonal and the base of the monitor?
5. How would you calculate the area of the screen given the width and height?

Tip: When solving right triangles, always check if you can use the Pythagorean theorem before moving to more advanced methods like trigonometry.