Answer :
Final answer:
Using the Pythagorean theorem with the aspect ratio 4:3, the calculated length of a 62" TV is found to be 49.6 inches, which does not match any of the provided answer choices, indicating a typo or miscalculation in the options.
Explanation:
The question involves calculating the length of a TV given its diagonal measurement and its aspect ratio. An aspect ratio of 4:3 means that for every 4 units of length, there are 3 units of height. To solve for the length of the TV, we can use the Pythagorean theorem in the context of the aspect ratio where 4 and 3 are the lengths of the legs and the 62" TV is the diagonal (hypotenuse).
Let's call the length L and the height H. Since the aspect ratio is 4:3, we have L/4 = H/3. To find L, we use the formula involving the diagonal D: L² + H² = D², where D is 62". From L/4 = H/3, we can solve for H as (3/4)*L. Substituting into the Pythagorean theorem gives L² + ((3/4)*L)² = 62². Solving for L gives L = 49.6 inches. The closest answer choice is (a) 46.5 inches, but this contains a slight error, so we must conclude there is a typo or miscalculation in the provided choices.
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