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
If the diagonal d of the box needs to be at least 41.5 inches, we can use the Pythagorean theorem to calculate the minimum dimensions of the box.
Let the length of the box be l, the width be w, and the height be h.
Using the Pythagorean theorem, we have:
d^2 = l^2 + w^2 + h^2
Substitute d = 41.5 inches:
(41.5)^2 = l^2 + w^2 + h^2
1712.25 = l^2 + w^2 + h^2
One possible set of dimensions that satisfies the condition is:
l = 20 inches, w = 20 inches, h = 21 inches
Plugging in these values:
(20)^2 + (20)^2 + (21)^2 = 400 + 400 + 441 = 1241
Since 1241 > 1712.25, the dimensions of the box are acceptable.
Therefore, a possible set of dimensions for the box with a diagonal of at least 41.5 inches is:
Length: 20 inches
Width: 20 inches
Height: 21 inches