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I have a question regarding triangles which is puzzling me:

In triangle PQR , PR=7 and PQ=4.5 . Which of the following cannot represent the length of QR ? a)2.0 , b)3 , c)3.5 , d)4.5 , e)5.0

Any suggestions ?

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What do you know about the sum of the sides of a triangle with respect to the remaining side? –  Pedro Tamaroff Jun 18 '12 at 21:16

2 Answers 2

up vote 2 down vote accepted

The sum of the two smaller sides must be greater than the last side.
So 2 can't be the length of QR : 2+4.5=6.5<7

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4  
Not surprisingly, this restriction is called the triangle inequality. –  lhf Jun 18 '12 at 21:17
    
Thanks for pointing that out.. I'll definitely keep this in mind –  MistyD Jun 18 '12 at 21:18

Any set of three lengths can represent the sides of a triangle provided the largest is smaller than the other two combined.

Therefore, the answer is (a) 2.0. The length PR of 7 is too long to support sides of 4.5 and 2.0.

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