SOLUTION: A rhombus has side lengths of 25. What could be the lengths of the diagonals?

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Question 1141617: A rhombus has side lengths of 25. What could be the lengths of the diagonals?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
From 0 to (25+25) = 50 units, exclusive.


ANSWER.  From 0 to 50, exclusive the ends of this interval.


HINT.  Apply the triangle inequalities.


Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
We start out with a square (which IS a rhombus for all sides are equal in
length. That's when the diagonals are equal in length, which, by the
Pythagorean theorem equal to 5%2Asqrt%282%29.
c%5E2=a%5E2%2Bb%5E2
c%5E2=25%5E2%2B25%5E2
c%5E2=25%5E2%2A2
c=sqrt%2825%5E2%2A2%29
c=5%2Asqrt%282%29

Then as we decrease the angle on the bottom left and increase the angle on
the bottom right, the green diagonal increases to 25+25 or 50, but never
quite gets to 50, for if it did, we'd only have a line segment 50 units
long.  The red diagonal shrinks to 0 but never quite gets to 0 for the same
reason.




Answer: the lengths of a diagonal can only be in the open interval from 0 to 50.  In interval notation that is (0,50) or 0 < x < 50.

Edwin