Final answer:
Jane would need to buy a screen with a diagonal size of approximately 56 inches. The calculation uses the Pythagorean theorem on the given width and height, which does not match any of the provided options A to D.
Step-by-step explanation:
Jane would like to have a screen 46 inches wide and 32 inches high. To determine the diagonal screen size she would need to buy, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate it:
- Width (W) = 46 inches
- Height (H) = 32 inches
We then apply the Pythagorean theorem to find the diagonal (D):
D² = W² + H²
D² = (46²) + (32²)
D² = 2116 + 1024
D² = 3140
D = √3140
D ≈ 56 inches
So, the screen size she needs to buy is approximately 56 inches diagonal. None of the options A through D is correct, as the closest standard size to 56 inches would typically be a 55-inch or 57-inch screen, depending on manufacturer standards.