One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. the perimeter is 38 cm. find the dimensions of the triangle.

Let's assume that the lengths of the sides of the triangle are x, y, z. Where x is the longest and z is the shortest.

y = z +4 (as this side is longer than the shortest by 4cm)> equation 1
y = x - 2 (as this side is shorter than the longest by 2cm)---> equation 2
x= y+2  (from equation 2 sub in 3)
x + y + z =38 > equation 3

(y+2)+ y + z =38
2 y +2 +z =38 (by subtracting both sides by 2)
2 y + z = 36 > equation 4
from equation # 1
y = z+4 
y - z =4 (by adding this equation with equation number 4)

3y =36+4 =40
y = 40/3 = 13.3333 cm (sub in equation 1 and 2)
z = 13.3333-4 =9.3333 cm (from equation 1)

x= y+2 = 13.3333+2 = 15.3333cm