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Answer :
Final answer:
The inner height of the box can be calculated using the Pythagorean theorem in 3 dimensions. The inner height of the box is 9cm.
Explanation:
The rod can be considered as the diagonal of the 3D box, which can be calculated using the Pythagorean theorem in 3 dimensions. It looks like the formula (Length2 + Breadth2 + Height2) = Diagonal2.
Substituting the given length and breadth (12cm and 8cm) and the longest rod (17cm), the equation becomes (122 + 82 + Height2) = 172. Or, (144 + 64 + Height2) = 289.
Solving this equation, we get Height2 = 289 - 144 - 64 = 81. Therefore, Height = √81 = 9cm.
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