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
20 inches, 21 inches, 26 inches
20 inches, 20 inches, 27 inches
21 inches, 24 inches, 26 inches
23 inches, 24 inches, 25 inches
explain which one is correct
To calculate the length of the diagonal of a rectangular box, you can use the formula: d = √(l^2 + w^2 + h^2) where d is the diagonal, l is the length, w is the width, and h is the height.
Given that the diagonal d should be at least 41.5 inches, we can plug in the values for each of the options:
1. For 20 inches, 21 inches, 26 inches:
d = √(20^2 + 21^2 + 26^2) = √(400 + 441 + 676) = √1517 ≈ 38.95 inches
This option does not meet the requirement.
2. For 20 inches, 20 inches, 27 inches:
d = √(20^2 + 20^2 + 27^2) = √(400 + 400 + 729) = √1529 ≈ 39.1 inches
This option also does not meet the requirement.
3. For 21 inches, 24 inches, 26 inches:
d = √(21^2 + 24^2 + 26^2) = √(441 + 576 + 676) = √1693 ≈ 41.18 inches
This option also does not meet the requirement.
4. For 23 inches, 24 inches, 25 inches:
d = √(23^2 + 24^2 + 25^2) = √(529 + 576 + 625) = √1730 ≈ 41.60 inches
This option meets the requirement of having a diagonal of at least 41.5 inches.
Therefore, the correct answer is 23 inches, 24 inches, 25 inches.