Question

This monitor has a diagonal length of 19 inches and an aspect ratio of 5:4. What are the width and height of the monitor? Round to the nearest tenth of an inch.

Answer 1

Rounded to the nearest tenth of an inch the Witdth of the monitor is 14.8 inches while the Height of the monitor is 11.9 inches.

Explanation:

The aspect ratio is defined as:

"The proportional relationship between the width and height of an image"

It is usually expressed in a mathematical language as:

$x:y \\ \\ x: \ Width \\ \\ y: \ Height$

So, it is true that:

$x:y=5:4 \\ \\ or: \\ \\ \frac{x}{y}=\frac{5}{4} \\ \\ \therefore x=\frac{5y}{4}$

In this case, we know that the monitor has a diagonal length (D):

$D=19in$

So, by Pythagorean theorem:

$D^2=361 \\ \\ 361=x^2+y^2 \\ \\ Since \ x=\frac{5y}{4}$

$D^2=361 \\ \\ 361=x^2+y^2 \\ \\ Since \ x=\frac{5y}{4} \\ \\ 361=\left(\frac{5y}{4}\right)^2+y^2 \\ \\ 361=\frac{25y^2}{16}+y^2 \\ \\ \frac{41}{16}y^2=361 \\ \\ y^2=\frac{261\times 16}{41} \\ \\ y=\sqrt{140.87} \\ \\ y=11.869in$

Finding x:

$x=\frac{5(11.869)}{4} \\ \\ x=14.836in$

Finally, rounded to the nearest tenth of an inch the Witdth of the monitor is 14.8 inches while the Height of the monitor is 11.9 inches.

Learn more:

Pythagorean Theorem: brainly.com/question/10182890

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