How do I find the dimensions of the triangle if the perimeter is 26cm and what does x represent as?

Question

The sides of a triangle are 2x + 1, 3x - 4 and x + 5. Find the dimensions of the triangle if the perimeter of the triangle is 26cm.

Answer 1

2x+1 + 3x-4 +x+5 =26

6x = 26 -2 = 24

x = 24/6 = 4

sides are 9, 8 and 9 they sum to 26

two sides re the same, each = 9 cm

let's say the perimeter had been 32 instead of 26

then 6x = 32-2= 30 and x = 5

the sides would be 11,11 and 10

if the perimeter had been 38

then 6x=36, x = 6

and the sides would be 13, 14, and 11

the role of x means x>4/3 given the 2nd side formula, with the two other sides are > 11/3 and > 19/3

that makes the perimeter > 10

the sides are not in a constant ratio.

but for any triangle the any side is greater than the sum of the other two sides

x+5> 2x+1 + 3x-4

8> 4x

2>x

x>2

that means the 3 sides have minimums of 2, 5 and 7

and the perimeter is a minimum 14

when 2<x< 4 x+5 is the largest side

when 4<x<5 2x+1 is the largest side

when x>5 3x-4 is the largest side

at x=4 (with perimeter = 26) it's a tie between x+5 and 2x+1 for longest side