To find the length of the diagonal in a box, we can use the Pythagorean theorem, which states that the square of the length of the diagonal (d) is equal to the sum of the squares of the length (l), width (w), and height (h) of the box.
So, d^2 = l^2 + w^2 + h^2
Given that d ≥ 41.5 inches, let's calculate the values for each option:
A: l=20, w=21, h=26
d^2 = 20^2 + 21^2 + 26^2
d^2 = 400 + 441 + 676
d^2 = 1517 which is less than 41.5^2
B: l=21, w=24, h=26
d^2 = 21^2 + 24^2 + 26^2
d^2 = 441 + 576 + 676
d^2 = 1693 which is greater than 41.5^2
C: l=23, w=24, h=25
d^2 = 23^2 + 24^2 + 25^2
d^2 = 529 + 576 + 625
d^2 = 1730 which is greater than 41.5^2
D: l=20, w=20, h=27
d^2 = 20^2 + 20^2 + 27^2
d^2 = 400 + 400 + 729
d^2 = 1529 which is greater than 41.5^2
Therefore, the correct answer is option A: a box with dimensions 20 inches, 21 inches, and 26 inches would have a diagonal length of at least 41.5 inches.
If you want the diagonal, d, to be at least 41.5 inches, what would be a possible length, width, and height for a box?
A: 20 inches, 21 inches, 26 inches.
B: 21 inches, 24 inches, 26 inches.
C: 23 inches, 24 inches, 25 inches.
D: 20 inches, 20 inches, 27 inches.
1 answer
1 answer