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)
21 inches, 24 inches, 26 inches
20 inches, 20 inches, 27 inches
20 inches, 21 inches, 26 inches
23 inches, 24 inches, 25 inches
The formula to calculate the diagonal of a rectangular box is: d = √(l^2 + w^2 + h^2), where l, w, and h are the length, width, and height of the box respectively.
Let's try the possible combinations of length, width, and height:
1. For 21 inches, 24 inches, 26 inches:
d = √(21^2 + 24^2 + 26^2) = √(441 + 576 + 676) = √1693 ≈ 41.16 inches
2. For 20 inches, 20 inches, 27 inches:
d = √(20^2 + 20^2 + 27^2) = √(400 + 400 + 729) = √1529 ≈ 39.10 inches
3. For 20 inches, 21 inches, 26 inches:
d = √(20^2 + 21^2 + 26^2) = √(400 + 441 + 676) = √1517 ≈ 38.94 inches
4. For 23 inches, 24 inches, 25 inches:
d = √(23^2 + 24^2 + 25^2) = √(529 + 576 + 625) = √1730 ≈ 41.58 inches
Among the options, the closest to a diagonal of at least 41.5 inches is the box with dimensions 23 inches, 24 inches, and 25 inches.