Question

two sides of a triangle is 3.7 and 8.2 what is the third length

Answer 1

To determine if a triangle can be formed with two sides of lengths 3.7 and 8.2, we can use the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must be satisfied:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In this case, let \(a = 3.7\) and \(b = 8.2\), and let \(c\) be the length of the third side.

Using the triangle inequalities:

1. \(3.7 + 8.2 > c\) → \(c < 11.9\)
2. \(3.7 + c > 8.2\) → \(c > 4.5\)
3. \(8.2 + c > 3.7\) → \(c > -4.5\) (This condition is always satisfied given \(c > 4.5\))

From the inequalities, we find that:

\[
4.5 < c < 11.9
\]

Thus, the length of the third side \(c\) must be more than 4.5 and less than 11.9 for a triangle to be formed with the two given sides.