Question

Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?

Answer 1

From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side

So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So

`\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}`

So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.

The answer is option C