A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is 16:9. What is the length diagonal of the screen, to the nearest whole inch.
W = Wide
H = height
D = Diagonal
W / H = 16 / 9
20 / H = 16 / 9 Multiply both sides by 9
20 * 9 / H = 16 * 9 / 9
180 / H = 16 Multiply both sides by H
180 * H / H = 16 * H
180 = 16 H Divide both sides by 16
180 / 16 = 16 H / 16
11.25 = H
H = 11.25 in
Pythagorean theorem :
D = sqroot ( W ^ 2 + H ^ 2 ) =
sqroot ( 20 ^ 2 + 11.25 ^ 2 ) =
sqroot ( 400 + 126.5625 ) =
sqroot ( 526.5625 ) =
22.9469497 in
approx. 23 in
To find the length of the diagonal of the screen, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides.
In this case, the width of the screen is one side of the right triangle, and the height of the screen is the other side. Let's call the width "w" and the height "h".
Given that the aspect ratio is 16:9, we can set up the following equation:
w/h = 16/9
Cross-multiplying gives us:
9w = 16h
Simplifying, we have:
h = (9/16)w
Now, we can substitute the width of the screen, which is 20 inches, into this equation:
h = (9/16) * 20
h = 11.25 inches (approximately)
Now, we have the width (w = 20 inches) and height (h = 11.25 inches) of the screen. We can use the Pythagorean theorem to find the length of the diagonal (d) as follows:
d^2 = w^2 + h^2
Substituting the values:
d^2 = 20^2 + 11.25^2
d^2 = 400 + 126.5625
d^2 = 526.5625
Taking the square root of both sides, we find:
d ≈ 22.94 inches
Rounding to the nearest whole inch, the length diagonal of the screen is approximately 23 inches.
To find the length of the diagonal of the computer monitor, we can use the Pythagorean theorem. According to the theorem, the square of the length of the hypotenuse (diagonal) of a right-angled triangle is equal to the sum of the squares of the other two sides.
In this case, we know the width of the screen is 20 inches, and the aspect ratio is 16:9. To determine the height of the screen, we can use proportions.
Since the aspect ratio represents a ratio of width to height, we can set up the following proportion:
Width / Height = 16 / 9
Substituting the known values:
20 / Height = 16 / 9
Now we can solve for the height:
Height * 16 = 20 * 9
Height = (20 * 9) / 16
Height = 11.25 inches (approximately)
Now that we have the width and height of the screen, we can use the Pythagorean theorem to find the length of the diagonal (D):
D^2 = Width^2 + Height^2
D^2 = 20^2 + 11.25^2
D^2 = 400 + 126.56
D^2 = 526.56
D = √526.56
D ≈ 22.94 inches
Therefore, the length of the diagonal of the screen is approximately 23 inches (to the nearest whole inch).