Final answer:
The largest HD TV that fits within a 5 feet wide and 4 feet high space on the wall is a 75-inch TV, which measures 65.625 inches wide and 37.125 inches high. The area of this TV is 2438.5 square inches.
Step-by-step explanation:
The student is attempting to determine the largest HD TV size that can fit within a specific area on a wall with dimensions of 5 feet in width and 4 feet in height. HD TVs have an aspect ratio of 16:9. To find the largest TV that can fit, we need to calculate the width and height dimensions of each TV option, then check which of these can fit within the wall space while adhering to the size parameters given.
Given the aspect ratio of 16:9, for any TV size, the width to height ratio should be 16/9. For instance, a 55-inch TV would have dimensions that, when the diagonal is calculated using the Pythagorean theorem on a 16:9 rectangle, would show width and height measurements proportionate to this aspect ratio. You do this by setting up the equation √((width)^2 + (height)^2) = (diagonal), with width and height having the ratio of 16:9. The resulting width and height are then compared to the available wall space dimensions. You should choose the largest TV whose dimensions do not exceed the wall space dimensions. Then, you calculate the area using the formula for the area of a rectangle (width x height).
Reviewing the options given by the student, the 75-inch TV, with a width of 65.625 inches (approximately 5.47 feet) and height of 37.125 inches (approximately 3.09 feet), fits within the available space. Therefore, option (c) is appropriate as the width and height do not exceed the 5 feet by 4 feet wall space.
The area for this TV would be calculated by multiplying the width by the height: 65.625 inches * 37.125 inches, which equals 2438.5 square inches. This area is specific to the TV and does not represent the total area of the space on the wall.