To determine the measure of the third side of a triangle with sides of length 1 cm and 13 cm, we can use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let the sides be:
- Side A = 1 cm
- Side B = 13 cm
- Side C = the unknown third side
We need to satisfy the following inequalities:
-
\( A + B > C \)
\( 1 + 13 > C \)
\( 14 > C \)
So, \( C < 14 \). -
\( A + C > B \)
\( 1 + C > 13 \)
\( C > 12 \). -
\( B + C > A \)
\( 13 + C > 1 \)
This inequality will always be true since \( C \) and \( 13 \) are both positive.
From inequalities 1 and 2, we have:
- \( 12 < C < 14 \)
Since \( C \) must be a whole number, the only value that satisfies this is:
- \( C = 13 \).
Therefore, the measure of the third side can be 13 cm.