Final answer:
To find the length of the larger LED TV, we set up a quadratic equation using the relationship between the areas of the larger and smaller TVs and their length-width difference. Solving the equation, we determine the length of the larger TV to be 48 inches.
Step-by-step explanation:
The question is a classic example of a quadratic equation problem, where we are given the area of a smaller and a larger TV's screen and need to find the dimensions of the larger TV. We are told that the area of the larger TV is 1200 square inches more than the area of a smaller TV and that the larger TV's length is 8 inches more than its width. To solve for the dimensions, let's assume the width of the larger TV is x inches. This makes the length x + 8 inches. Therefore, the area of the larger TV's screen would be x(x + 8) square inches. The area of the smaller TV is given as 720 square inches, so the larger TV's area would be 720 + 1200 = 1920 square inches. Setting up the equation, we get:
x(x + 8) = 1920
Expanding and rearranging the quadratic equation gives us:
x2 + 8x - 1920 = 0
Solving this quadratic equation, we find the width of the larger TV to be 40 inches. Thus, the length, being 8 inches more, is 48 inches. The correct answer is B. 48 in.