Question
Is there a triangle whose sides have lengths $10.2 \ cm, 5.8 \ cm$ and $4.5 \ cm?$
✓
Answer
Suppose such a triangle is possible. Then the sum of the lengths of any two sides would be greater than the length of the third side. Let us check this.
Is $4.5 + 5.8 > 10.2?$ Yes
Is $5.8 + 10.2 > 4.5?$ Yes
Is $10.2 + 4.5 > 5.8?$ Yes
Is $4.5 + 5.8 > 10.2?$ Yes
Is $5.8 + 10.2 > 4.5?$ Yes
Is $10.2 + 4.5 > 5.8?$ Yes
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