Answer:
26.8 in
Step-by-step explanation:
The red dashed line is the hypotenuse of the right triangle with one leg equal to 24 inches and the other leg equal to 12 inches. Its length is given by the Pythagorean theorem:
space diagonal = √(24^2 +12^2) = √(720) = 12√5
space diagonal ≈ 26.83 . . . inches
The length of the longest item that will fit in the box is about 26.83 inches.
