Hi Destiny
Based on the information above there can be many triangles formed from that date according to the Inequality Rule for triangles; is there any more information that you need to give for the question? If not, please see below:
Sides are 28, 30, and 31
Sides can be 29, 28 and 32
Given Perimeter = 89 cm and
Perimeter of a triangle = sum of all the sides of the triangle
Longest side is 3 cm longer than shorter side
According to the rule below we can set up everything in terms of the shorter side x
You have several choices based on the Triangle Inequality: which states that the sum of the lengths of any 2 sides of a triangle must exceed the length of the third side.
Let
x = shorter side
y = Longest side = x + 3
z = the remaining side
According to the rule above
x + y = x + x + 3 > z
x + z > y > x + 3
y + z = x + 3 + y > x
Since y is the longest side
z <= y; and therfore <= x + 3 this would be a Isosceles Triangle when z = y
Since x is the shorter side
z> = x this would would also include an Isosceles Triangle when z = x
This would imply that side z could be
x + 1
x + 2
I will try one of the cases above and select
z = x + 2
89 = x + x + 2 + x + 3
89 = 3x + 5
89 - 5 = 3x
84 = 3x
84/3 = x
28 = x
28 + 2 = x + 2 = z
30 = z
28 + 3 = x + 3 = y
31 = y
28 + 30 + 31 = 89
You can try the other two cases where z = y or z = x.
There is one other case, your question indicated that there is a shorter side and a longest side. It didn't give a definite shortest side which would imply that z could possibly be shorter than x; meaning z could be the shortest side z < x
z = x - 1
Would give the following possible triangle
x + x -1 + x + 3 = 89
3x + 2 = 89
3x = 87
x = 87/3
x = 29
x + 3 = 29 + 3 = 32 = y
x - 1 = 29 - 1 = 28 = z
