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0.5 < x < 16.5 given: Two sides of triangle: 8.0 units and 8.5 units Measure of third side = x According to the triangle's inequality, Sum of any two sides > third side. (i) Difference between the sides < third side. (ii) If x is the third side, then x < 8+8.5 [Using (i)] i.e. x< 16.5 Also, x > 8.5-8 [Using (ii)] i.e. x> 0.5 Hence, Range of possible sizes for side x would be 0.5 < x < 16.5.
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