Find the maximum length of a rod that can be placed in a box of dimension 10 cm × 15 cm × 20 cm.
Question
Solution
The maximum length of a rod that can be placed in a box is the diagonal of the box. This can be calculated using the Pythagorean theorem in three dimensions, which states that the diagonal of a box (d) is equal to the square root of the sum of the squares of the length (l), width (w), and height (h) of the box.
In this case, the length is 10 cm, the width is 15 cm, and the height is 20 cm.
So, the diagonal of the box (d) is equal to √(l² + w² + h²) = √(10² + 15² + 20²) = √(100 + 225 + 400) = √725 = approximately 26.91 cm.
Therefore, the maximum length of a rod that can be placed in the box is approximately 26.91 cm.
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