triangles with sides of integral length with a particular longest side (or sides)?

Question

for a particular longest side, how must the lengths of the sides of the triangle be related to ensure that they form a triangle?

for a particular longest side, how can you predict the number of possible triangles?

for a particular longest side, how many different perimeters are possible?

for a particular longest side, how can you predict the maximum perimeter? minimum perimeter?

for a particular longest side, how can you predict the maximum area? minimum area?

is it possible for the numerical value of the area to equal that of perimeter?

pls help homework.

Answer 1

in any triangle with sides a, b, and c
You must have this situation to have a triangle.
a + b > c
b + c > a
a + c > b
When you start plugging in numbers you realize that sometimes you have a good range of possibilities for the third side. Then you can start using the other situations you mention.

Answer 2

X=length of shortest area X+4=length of area A 2X=length of area B X+(X+4)+2X=40 4 ==> 4X+4=40 4 ==> 4X=40 ==> X=10 short area = 10 meters area A = X+4 = 14 meters area B = 2X = 20 meters