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)
Responses
21 inches, 24 inches, 26 inches
21 inches, 24 inches, 26 inches
20 inches, 20 inches, 27 inches
20 inches, 20 inches, 27 inches
23 inches, 24 inches, 25 inches
23 inches, 24 inches, 25 inches
20 inches, 21 inches, 26 inches
20 inches, 21 inches, 26 inches
In order to calculate the diagonal of a rectangular box, you can use the formula: d = √(l^2 + w^2 + h^2) where l is the length, w is the width, h is the height, and d is the diagonal.
Let's calculate the diagonal for each of the given options:
1. For (21, 24, 26):
d = √(21^2 + 24^2 + 26^2) = √(441 + 576 + 676) = √(1693) ≈ 41.16 inches
2. For (20, 20, 27):
d = √(20^2 + 20^2 + 27^2) = √(400 + 400 + 729) = √(1529) ≈ 39.11 inches
3. For (23, 24, 25):
d = √(23^2 + 24^2 + 25^2) = √(529 + 576 + 625) = √(1730) ≈ 41.62 inches
4. For (20, 21, 26):
d = √(20^2 + 21^2 + 26^2) = √(400 + 441 + 676) = √(1517) ≈ 38.94 inches
Therefore, the possible length, width, and height for the box for the diagonal to be at least 41.5 inches would be (23 inches, 24 inches, 25 inches).