I have a box. The two dimensions of the box are 4” and 3”.
Compute the third dimension of the box so that the space diagonal of the box is
an integer.
Answer: 12
inches. The diagonal of the end is 5. Therefore the space diagonal will be the hypotenuse
of a right angle, one of whose legs is 5, the other an integer.
Three numbers, known as the Pythagorean Triples, can be
represented by:
m1 ½ (m¹ -1) and ½ (m² +1) because
m₂+ (½ (m² -1 ) )² =
( ½ (m² + 1 ) ) ²
5² + 12² = 13². The other dimension is 12 inches, Therefore
the space diagonal is 13 inches.
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