SOLUTION: Find the length of the longest stick that will fit in a 4 cm by 6 cm by 12 cm box.

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Question 932918: Find the length of the longest stick that will fit in a 4 cm by 6 cm by 12 cm box.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The length (in cm) is .

THE EXPLANATION:
Let's say the box is sitting on one of the rectangular sides that measure 6 cm by 12 cm.
We call that the base of the box.
The diagonal splits that base into 2 right triangles with legs measuring 6 cm by 12 cm.
The length of that diagonal, green%28d%29 cm, according to the Pythagorean theorem, is such that
green%28d%29%5E2=6%5E2%2B12%5E2 .

That diagonal is perpendicular to one of the vertical 4-cm long edges of the box.
The longest possible stick, of length red%28s%29 cm, stick will form a right triangle with the diagonal of the base and a vertical edge.
This is what the (see through) box looks like:

According to the Pythagorean theorem,
red%28s%29%5E2=4%5E2%2Bgreen%28d%29%5E2
red%28s%29%5E2=4%5E2%2B6%5E2%2B12%5E2
red%28s%29=sqrt%284%5E2%2B6%5E2%2B12%5E2%29