Question

The perimeter of a given is an integer. the length of side one is 4 times the length of side 2. side three is 33. what is the largest and smallest possible perimeter

Answer 1

I assume this is a triangle.
the sum of two sides of a triangle has to be larger than the third side, and the difference has to be smaller than the third side
the two unknown sides are x and 4x
x+4x>33 => x>6.6
4x-x<33 => x<11
6.6<x<11
because the perimeter is an integer, the smallest x is 7 and the largest is 10
therefore the largest perimeter is 10+40+33=83
the smallest perimeter is 7+28+33=68