1 Answer

Ngawang · Answer 1 · 2023-03-07T21:13:09+0000

For a, b, and c to be the lengths of a triangle they must satisfy the following system of inequalities:

$\begin{gathered} a+b>c, \\ a+c>b, \\ b+c>a\text{.} \end{gathered}$

Now, notice that:

$\begin{gathered} 7+54>45, \\ 45+54>7,\text{ } \\ 45+7=52<54. \end{gathered}$

Since the given numbers do not satisfy the last inequality, then they cannot be the lengths of a triangle.

Answer: No it is not possible to construct a triangle with lengths 7, 54 and 45, because:

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