# Geometria

Two sides of a triangle are 11cm and 16cm what is the range of possible lengths for the third side

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1. third side --- x

by properties of sides of a triangle:
x+11>16 and x+16 > 11 and 11+16> x
x > 5 and x > -5 , (no argument there) and x < 27
so x > 5 and x < 27 or
5 < x < 27

in words: the third side must be greater than 5 but less than 27

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2. the 3rd side must be shorter than the sum of the 1st two sides
... and longer than their difference

(11 + 16) > s > (16 - 11)

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