Question

the perimeter of a triangle is between 10 and 24 feet inclusive. List all possible lengths of the longest sides of the triangle ?

Answer 1

This appears to be a calculus problem but I am unsure how to frame it. I can tell you logically that if one of the sides is set to 0, the hypotenuse would be equal to the other side. This caps the maximum range at being 5-12 ft.
In the case of the 10 ft perimeter:
\[\lim_{opposite \rightarrow 0}hypotenuse = 5 ft\]
In the case of the 24 ft perimeter:
\[\lim_{opposite \rightarrow 0} hypotenuse = 12 ft\]