What is the length of the longest toothpick which can be placed inside a rectangular box is 3cm × 5cm ×8cm ?

The maximum length of a toothpick that still fits the box is

Explanation: the longest straight distance within a rectangular box (prism) is its diagonal (in three dimensions), i.e., the path from one corner to its diagonally opposite corner.

The diagonal length in a two-dimensional rectangle can be calculated using the Pythagorean Theorem. There is a three-dimensional analog of that theorem for prisms. Let a,b,c be the sides of the prism. Then the following holds for the diagonal length d:

In order to answer the question we determine the length d:

i am sure it will be 90 degrees.

step-by-step explanation:

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