Richard draws a triangle in the dirt. Two of the sides of the triangle measure 14 inches and 6 inches. Which could be the length of the third side of Richard's triangle? (1 point) 7 inches 3 inches 0.20 inches ( 15 inches Check answer Remaining Attempts: 3

1. The triangle inequality 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. 2. Let the unknown side be \( x \). Given sides are 14 inches and 6 inches. 3. The triangle inequalities are: - \( 14 + 6 > x \) which simplifies to \( x < 20 \) - \( 14 + x > 6 \) which simplifies to \( x > 6 - 14 \) (but since \( 6 - 14 \) is negative, this inequality is always true for positive \( x \)) - \( 6 + x > 14 \) which simplifies to \( x > 14 - 6 \) so \( x > 8 \) 4. Combining these results, the third side must satisfy: \[ 8 < x < 20 \] 5. Checking the options: - 7 inches: Does not satisfy \( x > 8 \). - 3 inches: Does not satisfy \( x > 8 \). - 0.20 inches: Does not satisfy \( x > 8 \). - 15 inches: Satisfies \( 8 < 15 < 20 \). Thus, the length of the third side could be \( 15 \) inches.