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To find the length of each diagonal, we can use the Pythagorean theorem.
Let's label the length, width, and height as follows:
Length = l = 44 in
Width = w = 24 in
Height = h = 14 in
We can find the diagonal on the bottom face of the rectangular prism using the formula:
Diagonal = √(length^2 + width^2)
Diagonal = √(44^2 + 24^2)
= √(1936 + 576)
= √(2512)
≈ 50.1 in
Now, we can find the diagonal running from one bottom corner to the top opposite corner of the rectangular prism.
This diagonal can be found using the formula:
Diagonal = √(length^2 + width^2 + height^2)
Diagonal = √(44^2 + 24^2 + 14^2)
= √(1936 + 576 + 196)
= √(2708)
≈ 52 in
So, the length of each diagonal should be 50.1 inches and 52 inches, respectively.