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? Choose 1 answer: (A) 7.1 (B) 14.8 (C) 15.5 (D) 22.4

Question

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? Choose 1 answer: (A) 7.1 (B) 14.8 (C)  15.5 (D) 22.4

Bytelearn · Accepted Answer

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. 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. Diagonal (c) = 19 inches, so c^2 = 19^2 = 361. Height (a) = 11.9 inches, so a^2 = 11.9^2. Let's calculate a^2.Calculate Width Square: Calculating the square of the height: 11.9^2 = 141.61. 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. c^2 = a^2 + b^2 can be rearranged to find b^2: b^2 = c^2 - a^2. 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 = √219.39. Let's calculate the square root of 219.39.Calculating the square root of 219.39: b ≈ 14.8 inches. So, the width of the monitor is approximately 14.8 inches.

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