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) (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, cm, according to the Pythagorean theorem, is such that
.
That diagonal is perpendicular to one of the vertical 4-cm long edges of the box.
The longest possible stick, of length 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,
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