Question

How do I find the possible lengths for these measurements?

Answer 1

In general, the triangle inequality theorem states that if a, b, and c are the sides of a triangle,

`\begin{gathered} a+b>c \\ b+c>a \\ c+a>b \end{gathered}`

Therefore, in our case, since the dimensions of 7.5m and 4.8m are fixed,

`\begin{gathered} 7.5+4.8>x \\ 4.8+x>7.5 \\ x+7.5>4.8 \end{gathered}`

Solving the inequalities for x,

`\begin{gathered} \Rightarrow12.3>x \\ x>2.7 \\ x>-2.7 \end{gathered}`

Thus,

`\Rightarrow12.3>x>2.7`

In interval notation, the answer is (2.7, 12.3)