Question 557587: a square has side length 9 in, what is the lenght of the longest line segment that can be drawn between any two points of the square?
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
The longest line segment that can be drawn from any 2 points on a square,
must naturally be a diagonal of a square. No other possible line segment will be as long as any diagonal of the square.
You can test this out with any ruler, and any true square.
So, given a side of 9 cm, we can use the Pythagorean Theorem to find the length of the diagonal of the square.
 or 
Since we are dealing with distances, we can discard the negative solution.
 which is the exact answer
The longest line segment would be  cm.
Alternatively, we can find an approximation for this answer:
 cm
Using the familiar rules of geometry, and recognizing that a square is cut into two 45-45-90 triangles by a diagonal,
we could have immediately determined the length of the diagonal to be cm long.
But then we wouldn't have had the nice opportunity to use the Pythagorean Theorem!
I hope this helps! :)
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