Question

The three side lengths of a non-degenerate triangle are $x$, $x+5$ and $x+11$. Then $x$ cannot be .

• A. $4$
• B. $8$
• C. $7$
• D. $10$

Answer 1

The correct option is A $4$

From the "Inequality of a triangle" property of a triangle, we know that the sum of any two sides of the triangle must be greater than the third side.

If $x=7$,
the $3$ line segments would measure $7$, $12$ and $18$ respectively.
This is posible as the sum of the length of any two line segments is greater than the length of the third line segment. Hence, they can form a triangle and $x$ can be $7$.

If $x=4$,
the $3$ line segments would measure $4$, $9$ and $15$ respectively.
Since $4+9<15$, these line segments cannot form a triangle. Hence, $x$ cannot be $4$

If $x=8$,
the $3$ line segments would measure $8$, $13$ and $19$ respectively.
This is posible as the sum of the length of any two line segments is greater than the length of the third line segment. Hence, they can form a triangle and $x$ can be $8$.

If $x=10$,
the $3$ line segments would measure $10$, $15$ and $21$ respectively.
This is posible as the sum of of the length any two line segments is greater than the length of the third line segment. Hence, they can form a triangle and $x$ can be $10$.