Can atriangle be formed with side lengths of 5cm. 10cm and 15cm
2 answers:
Remember longest side must be less than the sum of the other 2 sides because if it is eqal than you get a line, and if it is longer, then you cannot connect the points longest side is 15 15<10+5 15<15 fasle no triangle can be formed
Theorem of cosine: a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc In this case: a=15 cm b=10 cm c=5 cm cos α=-(15²-10²-5²) / 2*10*5 cos α=-100 / 100 cos α=-1 A=arc cos -1=180º This is impossible, because: A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle). Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.
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