Question

teacher:stirewalt class:1st period math 2 spring 2025 lee4tvsp
student gentry, holden
describe the possible lengths for the third side of a triangle with two sides of 4 ft and 12 ft using a compound inequality. (hint: use < or > to submit your answer.)

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the sides of the triangle be $a = 4$, $b = 12$, and the third - side be $x$.

Step2: First inequality

$a + x>b$ and $a + b>x$ and $x + b>a$. From $a + x>b$, we have $4 + x>12$, which simplifies to $x>12 - 4$, so $x>8$.

Step3: Second inequality

From $x + a>b$, we also consider $x< a + b$. Substituting $a = 4$ and $b = 12$, we get $x<4 + 12$, so $x<16$.

Answer:

$8 < x < 16$