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Geometry - Ratios










































If a 20-inch monitor has a horizontal/vertical aspect ratio of 4:3, what are the hoizontal and vertical dimensions of the montior?

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Nov 07, 2011
Compute Dimensions from Aspect Ratio
by: Staff

Question:

If a 20-inch monitor has a horizontal/vertical aspect ratio of 4:3, what are the hoizontal and vertical dimensions of the montior?



Answer:

20-inch monitor measurements: diagonal measurement from corner to corner is 20 inches



Open the link shown below to view a diagram of the dimensions of a 20-inch wide screen monitor:

(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/dimensions-20-in-monitor-2011-11-07-01.png


The aspect ratio of 4:3 is the ratio of the width of the viewable image to the height of the viewable image. (this means the ratio of width to height is 4 ÷ 3, or 1.333?)

Mathematically, this aspect ratio can be diagrammed as multiples of x.

Open the link shown below to view a diagram of the aspect ratio:

(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/aspect-ratio-20-in-monitor-2011-11-07-01.png


As you can see, there are two right triangles.

You can solve for x using the Pythagorean Theorem (Pythagorean Equation):

a² + b² = c²


For this problem:

a = 3x

b = 4x

c = 20 inches, the diagonal


Substitute these values in the Pythagorean Equation

(3x)² + (4x)² = 20²


Solve for x

(3x)² + (4x)² = 20²

9x² + 16x² = 400


Combine like terms

25x² = 400


Divide each side of the equation by 25

25x² / 25 = 400 / 25

x² * (25 / 25) = 400 / 25

x² * (1) = 400 / 25

x² = 400 / 25

x² = 16


Take the square root of each side of the equation

√(x²) = √(16)

x = √(16)

x = 4 (x actually = ±4, but only the positive dimension can be used)


Compute the final dimensions:


Horizontal Dimension = 4x

Substitute the value of 4 for x

Horizontal Dimension = 4 * 4

Horizontal Dimension = 16 inches


Vertical Dimension = 3x

Substitute the value of 4 for x

Vertical Dimension = 3 * 4

Vertical Dimension = 12 inches




The final answer is:

Horizontal Dimension = 16 inches

Vertical Dimension = 12 inches


Check the results using the Pythagorean Equation:


(Horizontal Dimension)² + (Vertical Dimension)² = (Diagonal)²

(16)² + (12)² = (20)²

256 + 144 = 400

400 = 400 → dimensions of 16 inches by 12 inches are valid solutions






Thanks for writing.

Staff
www.solving-math-problems.com



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