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, 20 inches, 27 inches
20 inches, 20 inches, 27 inches
20 inches, 21 inches, 26 inches
20 inches, 21 inches, 26 inches
21 inches, 24 inches, 26 inches
21 inches, 24 inches, 26 inches
23 inches, 24 inches, 25 inches
3 answers
23 inches, 24 inches, 25 inches
could you work it out
To find the length of the diagonal d of the box, we can use the formula for the diagonal of a rectangular prism:
d = sqrt(l^2 + w^2 + h^2)
Given that we want the diagonal to be at least 41.5 inches, we can plug in the values:
41.5 ≤ sqrt(23^2 + 24^2 + 25^2)
41.5 ≤ sqrt(529 + 576 + 625)
41.5 ≤ sqrt(1730)
Now, find the square root of 1730:
sqrt(1730) ≈ 41.59
Therefore, the dimensions of 23 inches, 24 inches, and 25 inches would satisfy the condition of having a diagonal of at least 41.5 inches.
d = sqrt(l^2 + w^2 + h^2)
Given that we want the diagonal to be at least 41.5 inches, we can plug in the values:
41.5 ≤ sqrt(23^2 + 24^2 + 25^2)
41.5 ≤ sqrt(529 + 576 + 625)
41.5 ≤ sqrt(1730)
Now, find the square root of 1730:
sqrt(1730) ≈ 41.59
Therefore, the dimensions of 23 inches, 24 inches, and 25 inches would satisfy the condition of having a diagonal of at least 41.5 inches.