Question

12 with the side lengths given, find the possible side lengths for the third side. select all that apply.
16 mm and 28 mm
a 6
b 12
c 16
d 18
e 25
f 42
g 46

Explanation:

Step1: Apply triangle inequality theorem

For a triangle with sides $a$, $b$, $c$, the sum of any two sides must be greater than the third side. Let the given sides be $a=16$ mm, $b=28$ mm, and the third side be $x$. First, calculate the lower bound: $b - a < x$
$\implies 28 - 16 < x$
$\implies 12 < x$

Step2: Calculate the upper bound

$x < a + b$
$\implies x < 16 + 28$
$\implies x < 44$

Step3: Identify valid values

Find values from options that satisfy $12 < x < 44$.

Answer:

C. 16, D. 18, E. 25, F. 42