Question

Find the length of the third side. If necessary, round to the nearest tenth.
25
24

Answer 1

To determine the length of the third side of a triangle when the lengths of two sides are given (25 and 24), we can apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let \( c \) represent the length of the third side. The inequalities can be expressed as follows:

1. \( 25 + 24 > c \)
2. \( 25 + c > 24 \)
3. \( 24 + c > 25 \)

Now, we will solve these inequalities:

1. From \( 25 + 24 > c \):
\[
49 > c \quad \text{or} \quad c < 49
\]

2. From \( 25 + c > 24 \):
\[
c > 24 - 25 \quad \text{or} \quad c > -1 \quad \text{(always true since side lengths are positive)}
\]

3. From \( 24 + c > 25 \):
\[
c > 25 - 24 \quad \text{or} \quad c > 1
\]

Combining the last two valid inequalities, we find the range for \( c \):
\[
1 < c < 49
\]

Thus, the possible lengths for the third side \( c \) can be any value greater than 1 and less than 49. However, if you were looking for a specific length instead of a range, please provide additional conditions or information, such as whether this is a special type of triangle (e.g., a right triangle), which might help narrow down the possibilities.