Question

Can atriangle be formed with side lengths of 5cm. 10cm and 15cm

Answer 1

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

Answer 2

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.