Question

the size of a computer monitor is based on the diagonal length across the screen. The image shows a 24-inch monitor that is 13.6 inches tall. How wide is the monitor? Round to the nearest tenth of an inch.

Answer 1

Answer:

19.8 in

Step-by-step explanation:

Draw a diagram to represent the situation. It will be easier to see what you need to find. (See my diagram below). We are looking for side "w", the width of the computer monitor.

Notice half of the computer monitor is a right-angle triangle. In any right-angle triangle, we can use the Pythagorean Theorem when you have two sides and need to find one missing side. The formula is a² + b² = c².

"c" represents the hypotenuse, which is the longest side.

"a" and "b" are the two other sides, it doesn't matter which one is 'a' or 'b'.

In our problem, we have the hypotenuse, which is the diagonal of the rectangle. c = 24

We can call the height "a". a = 13.6, so we will be finding "b". b = w.

Use the Pythagorean Theorem and substitute a = 13.6, b = w, and c = 24.

a² + b² = c²

13.6² + w² = 24²

Now, isolate "w". Move everything else to the other side by cancelling them out with reverse operations.

13.6² - 13.6² + w² = 24² - 13.6²       Subtract 13.6²on both sides

w² = 24² - 13.6²

√w² = √(24² - 13.6²)    Square root both sides. √ and ² cancel out

w = √(24² - 13.6²)      "w" is isolated

Simplify the equation to solve for "w".

w = √(24² - 13.6²)         Square each number in the bracket

w = √(576 - 184.96)        Subtract within the bracket

w = √391.04           Square root the number

w = 19.7747314         Round up based on the second decimal place

w ≈ 19.8          Final value in inches

Include the units, inches, in the answer.

Therefore the width is 19.8 inches.

We rounded up because the second decimal place is 5 or greater. If the second decimal place was 4 or less, we would have rounded down, making the answer 19.7.