Question

A computer system is advertised with a 14-inch monitor. The measurement of the monitor is along the diagonal of the screen. The height of the monitor screen is 9 inches. What is the width of the monitor screen?

Answer 1

`sqrt115` inches or about `10.724` inches (rounded to the nearest thousandth's place).

Explanation:

To solve this problem we use the Pythagorean Theorem, shown here:

As you can see, we can solve the missing side of a right triangle using `color(red)(a)^2 + color(green)(b)^2 = color(blue)(c)^2` if we have the measurements of the other two sides.

In our problem, we have a diagonal (hypotenuse) of `14` inches. We also know that the height is `9` inches.

In the Pythagorean Theorem, that means we have `color(red)(a)` and `color(blue)(c)`.

So let's plug them into the formula:
`color(red)(9)^2 + color(green)(b)^2 = color(blue)(14)^2`

Simplify by squaring:
`81 + b^2 = 196`

Subtract `color(orange)81` from both sides of the equation:
`81 + b^2 quadcolor(orange)(-quad81) = 196 quadcolor(orange)(-quad81)`

`b^2 = 115`

Square root both sides:
`sqrt(b^2) = sqrt115`

`b = sqrt115` or about `10.724` (rounded to nearest thousandth's place)

Therefore, the width of the monitor screen is `sqrt115` inches or about `10.724` inches (rounded to the nearest thousandth's place).

Hope this helps!