Answer:
Only option C: The shortest side can equal 7 cm.
Step-by-step explanation:
Let the length of the shortest side be x cm, then the length of the longest side is 4x cm. Let the length of the middle side be y cm. Note that
The perimeter is
A. The value x cannot be 40 cm, because then y is negative
B. If the longest side is 30 cm long, then
But
This means that such triangle does not exist
C. If x=7 cm, then 4x=28 cm,
Since,
such triangle exists and this option is possible
D. If x=25 cm, then y is negative
E. If x=5 cm, then 4x=20 cm and
But this triangle does not exist, because