Question

Can a triangle have sides with the given lengths?a2 in, 4 in, 6 inYesNo

Answer 1

In general, if the sides of a triangle are a, b, and c, they must satisfy the inequalities below

`\begin{gathered} a,b,c\rightarrow\text{ sides of a triangle''} \\ \Rightarrow a+b>c \\ b+c>a \\ c+a>b \end{gathered}`

Therefore, in our case,

`\begin{gathered} 2+4>6\Rightarrow6>6\rightarrow False \\ 4+6>2\Rightarrow10>2\rightarrow True \\ 6+2>4\Rightarrow8>4\rightarrow True \end{gathered}`

The first inequality is false; thus, the triangle cannot exists. The answer is No.