Kaizen's rectangular computer monitor has a diagonal length of $19$ inches. If the height of the monitor is $11.9$ inches, which of the following is closest to the width of the monitor in inches? $\newline$ Choose $1$ answer: $\newline$ (A) $7.1$ $\newline$ (B) $14.8$ $\newline$ (C) $15.5$ $\newline$ (D) $22.4$

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Q. Kaizen's rectangular computer monitor has a diagonal length of

19

inches. If the height of the monitor is

11.9

inches, which of the following is closest to the width of the monitor in inches?

\newline

Choose

1

answer:

\newline

(A)

7.1

\newline

(B)

14.8

\newline

(C)

15.5

\newline

(D)

22.4

Use Pythagorean Theorem: We can use the Pythagorean theorem to find the width of the monitor. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ . In this case, the diagonal of the monitor is the hypotenuse, the height is one side, and the width we are looking for is the other side. $\newline$ Mathematically, this is expressed as $c^2 = a^2 + b^2$ , where $c$ is the diagonal, $a$ is the height, and $b$ is the width.
Calculate Diagonal and Height Squares: First, we need to square the length of the diagonal and the height to find the square of the width. $\newline$ Diagonal $c$ = $19$ inches, so $c^2 = 19^2 = 361$ . $\newline$ Height $a$ = $11.9$ inches, so $a^2 = 11.9^2$ . $\newline$ Let's calculate $a^2$ .
Calculate Width Square: Calculating the square of the height: $11.9^2 = 141.61$ . $\newline$ Now we have $a^2 = 141.61$ .
Use Pythagorean Theorem to Solve for Width Square: Next, we use the Pythagorean theorem to solve for $b^2$ , which is the square of the width. $\newline$ $c^2 = a^2 + b^2$ can be rearranged to find $b^2$ : $b^2 = c^2 - a^2$ . $\newline$ Substituting the values we have: $b^2 = 361 - 141.61$ .
Calculate Width: Calculating $b^2$ : $b^2 = 361 - 141.61 = 219.39$ . Now we have the value of $b^2$ .
Find Width: To find the width $b$ , we need to take the square root of $b^2$ . $b = \sqrt{219.39}$ .Let's calculate the square root of $219.39$ .
Find Width: To find the width $b$ , we need to take the square root of $b^2$ . $b = \sqrt{219.39}$ .Let's calculate the square root of $219.39$ .Calculating the square root of $219.39$ : $b \approx 14.8$ inches.So, the width of the monitor is approximately $14.8$ inches.