Question

Find the width and height of an older 72 inch television whose screen aspect ratio is 4:3. Remember, round your answer to one decimal place.

A. W = 246.4 and H = 138.6
B. W = 56 and H = 42
С. W = 138 and H = 246
D. W = 57.6 and H = 43.2

Answer 1

D. W = 57.6 and H = 43.2. The width and height of an older 72 inch television with a 4:3 aspect ratio are approximately 57.6 inches and 43.2 inches, respectively, which corresponds to option D.

Step-by-step explanation:

To find the width and height of an older television with a 72-inch diagonal and a 4:3 screen aspect ratio, we can use the Pythagorean theorem. The aspect ratio means that for every 4 units of width, there are 3 units of height, forming a right-angled triangle with these sides and the screen diagonal as the hypotenuse.

Let's denote the width as w and the height as h. The aspect ratio 4:3 can be represented as w/h = 4/3, which means w = (4/3)h. Using the Pythagorean theorem where the screen diagonal is 72-inches (d), we get w2 + h2 = d2. Plugging the aspect ratio into this equation, we have ((4/3)h)2 + h2 = 722.

Simplifying and solving for height, we get h ≈ 43.2 inches. Substituting this value back into the ratio w = (4/3)h, we find w ≈ 57.6 inches. Therefore, the correct answer is W = 57.6 and H = 43.2 rounded to one decimal place, which corresponds to option D.