If you want the diagonal, d, to be at least 41.5 inches, what would be a possible length, width, and height for the box?(1 point)Responses21 inches, 24 inches, 26 inches 21 inches, 24 inches, 26 inches20 inches, 20 inches, 27 inches20 inches, 20 inches, 27 inches20 inches, 21 inches, 26 inches20 inches, 21 inches, 26 inches 23 inches, 24 inches, 25 inches
In order to determine the possible length, width, and height for the box, we can use the Pythagorean theorem.
Let the length be L, the width be W, and the height be H. We want to find values that satisfy the equation:
L^2 + W^2 + H^2 = d^2
In this case, we are given that the diagonal d is at least 41.5 inches. Let's try the possible values given:
1. L = 21 inches, W = 24 inches, H = 26 inches
21^2 + 24^2 + 26^2 = 441 + 576 + 676 = 1693 inches
This is not greater than 41.5, so this set of values does not work.
2. L = 20 inches, W = 20 inches, H = 27 inches
20^2 + 20^2 + 27^2 = 400 + 400 + 729 = 1529 inches
This is not greater than 41.5, so this set of values does not work.
3. L = 20 inches, W = 21 inches, H = 26 inches
20^2 + 21^2 + 26^2 = 400 + 441 + 676 = 1517 inches
This is not greater than 41.5, so this set of values does not work.
4. L = 23 inches, W = 24 inches, H = 25 inches
23^2 + 24^2 + 25^2 = 529 + 576 + 625 = 1730 inches
This is greater than 41.5, so this set of values would work.
Therefore, a possible length, width, and height for the box to have a diagonal of at least 41.5 inches would be:
Length = 23 inches, Width = 24 inches, Height = 25 inches.