Question

A triangle has side lengths of $6$ inches and $9$ inches. If the third side is an integer, calculate the minimum possible perimeter of the triangle (in inches).

• A. $4$
• B. $15$
• C. $8$
• D. $19$
• E. $29$

Answer 1

The correct option is D $19$

Let the third side be $x$.
Sum of any two sides of a triangle is greater than the third side.

Hence, $6+x>9$ or $x>3$ and $6+9>x$ or $x<15$.

Therefore, $xϵ(3,15)$

Hence, the minimum possible integral value of $x$ is $4$.

Thus the minimum possible length of the third side is $4$.

Hence, the minimum possible perimeter is $4+6+9=19$ units.