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?

1 Answer
May 19, 2018

Answer:

#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:
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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!