Let's call the length of the rectangle "L" and the width "W".
From the problem, we know that:
- The perimeter of a rectangle is 2(L + W), so 2(L + W) = 52 (since "The perimeter of a rectangle is 52 cm")
- The width is 2 cm more than one-third of the length, so W = (1/3)L + 2 (since "Its width is 2 cm more than one-third of its length")
We can use substitution to solve for one of the variables. Substituting the second equation into the first equation, we get:
2(L + (1/3)L + 2) = 52
Simplifying the left side, we get:
2(4/3 L + 2) = 52
Multiplying both sides by 1/2, we get:
4/3 L + 2 = 26
Subtracting 2 from both sides, we get:
4/3 L = 24
Multiplying both sides by 3/4, we get:
L = 18
Now that we know L, we can use the second equation to solve for W:
W = (1/3)L + 2
W = (1/3)(18) + 2
W = 8
Therefore, the dimensions of the rectangle are 18 cm by 8 cm.