Which of the side lengths could form a triangle? A) 2 cm, 2 cm, 4 cm B) 3 cm, 5 cm, 10 cm C) 3 cm, 4 cm, 5 cm D) 4 cm, 8 cm, 15 cm Eliminate

Answer:  The correct option is (C) 3 cm, 4 cm, 5 cm. Step-by-step explanation:  We are given to select the correct side lengths that could form a triangle.We know thatthe sum of the lengths of any two sides of a triangle is always greater than the third side.That is, if a, b and c represents the lengths of three sides of a triangle, then we must have[tex]a+b>c,~~b+c>a,~~c+a>b.[/tex]Option (A) is a = 2 cm, b = 2 cm, c = 4 cm.We have[tex]a+b=2+2=4=c~~~\Rightarrow a+b=c.[/tex]Hence, this option is NOT correct.Option (B) is a = 3 cm, b = 5 cm, c = 10 cm.We have[tex]a+b=3+5=8<10=c~~~\Rightarrow a+b<c.[/tex]So, this option is NOT correct.Option (C) is a = 3 cm, b = 4 cm, c = 5 cm.We have[tex]a+b=3+4=7>5=c~~~\Rightarrow a+b>c,\\\\b+c=4+5=9>3=a~~~\Rightarrow b+c>a,\\\\c+a=5+3=8>4=b~~~\Rightarrow c+a>b.[/tex]So, this option is CORRECT.Option (D) is a = 4 cm, b = 8 cm, c = 15 cm.We have[tex]a+b=4+8=12<15=c~~~\Rightarrow a+b<c.[/tex]So, this option is NOT correct.Thus, (C) is the correct option.