Final answer:
To find the area of a 13-inch computer monitor with a height of 5 inches, we first used the Pythagorean theorem to calculate its width, which is 12 inches. Then, by multiplying the height and width, we determined that the screen's area is 60 square inches.
Step-by-step explanation:
The question asks us to find the area of a computer monitor based on its diagonal measurement and height. To solve this, we will use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the context of the monitor, the diagonal is the hypotenuse, and the height and width are the other two sides.
First, let's consider the monitor's measurements:
- Diagonal (d): 13 inches
- Height (h): 5 inches
We need to find the width (w). We can do this using the Pythagorean theorem:
d² = h² + w²
Plugging in our known values:
13² = 5² + w²
169 = 25 + w²
w² = 169 - 25
w² = 144
w = √144
w = 12 inches
Now that we have both the height and width, we can calculate the area of the screen:
Area = height × width
Area = 5 inches × 12 inches
Area = 60 square inches
The area of the screen is 60 square inches.