x - length of the shortest side
2x - length of the longest side
y - length of the third side
1) Longest side(2x) is "3 cm less than the sum of the lengths of the other two sides(x+y)" :
2x= x+y - 3 → x - y = - 3
2) "The perimeter of a triangle is 19 cm."
x + 2x + y = 19 → 3x + y = 19
3) We have a system of equations now.
x-y = -3
3x+y= 19
We can add these equations:
x-y+3x+y = -3 +19
4x = 16
x=4 (cm) is a shortest side.
2x = 2*4 = 8 (cm) is a longest side.
3x + y = 19 → 3*4 +y = 19 → 12 + y = 19 → y = 7 (cm) is a third side of the triangle.
