A nice geometry problem
Geometry
Level
3
Three sides of a quadrilateral are all positive integer and three of them are given to be . How many possible values are there for the fourth side?
29
30
28
27
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1 solution
The sides of length 10 and 5 joined together is 5 less than the 3rd side 20. So the 4th side has to be bigger than 5 (for 5 the quadrilateral reduces to a straight line, and for less than 5, the loop cannot be completed at all). Similarly on the bigger limit, the 4th side has to be less than 5+10+20, i.e. 35 (if it is 35, it reduces to a straight line and for longer than 35, the loop cannot be closed). So the 4th side can can take 29 different integral values from 6 to 34.