Question 14649: You have a triangle with sides 6, 7 and x. What is the maximum that x can be and why?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! There seems to be an error in your problem .There are 2 basic (inter-related)rules governing the dimensions of the 3 sides of a triangle for it to exist,that is for you to physically draw a triangle with those dimensions.They are
1. Sum of any 2 sides shall be greater than the third side and
2. Difference of any 2 sides shall be less than the third side.
Otherwise, what happens is that when you attempt to draw such a triangle , you will not be able to get the third vertex after having started with any 2 sides and 2 vertices.
Hence ,in our present problem ,since 2 sides are 6 & 7 b,the third side x shall be greater than 13 or less than 1 (ofcourse it cannot be zero or negative).That is x should lie between 9 and 1 or should be greater than 13.
Hence it is not correct to say that x has a maximum value .We can however say it has a minimum of zero in the lower range of number line and in that vicinity a local maximum of one and then again a minimum of 13 in the upper range of number line with no limit on maximum higher value beyond that.
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