Estonian Mathematical Olympiad

Let the sidelengths of the smaller rectangle (in cm) be $a$ and $b$. Then the sidelengths of the larger rectangle are $a+5$ and $b+5$. The area of the smaller rectangle is $ab$, whereas the area of the larger rectangle is $(a+5)(b+5)=ab+5a+5b+25$, which by the information given is equal to $ab+100$. Thus $5a+5b+25=100$, which yields $a+b=15$. Thus the perimeter of the smaller rectangle (in cm) is $2(a+b)=30$.