The perimeter is equal to the area The measurements on the sides of a rectangle are distinct integers. The perimeter and area of ​​the rectangle are expressed by the same number. Determine this number. 
Answer: 18 
It could be $4*4$ = $4+4+4+4$ but the answer is 18. 
Wait... Now that I noticed, the sides are different numbers. But I can't find a way to solve.

Let's see, let $x$ be the length of the one side and $y$ be the length of one of the adjacent sides. Then the perimeter of the rectangle is $P(x,y)=2x+2y$ and the area is $A(x,y)=xy$. So we need $P=A$ i.e. $2x+2y=xy$. Thta is, $$2x+2y=xy \Leftrightarrow 2x-xy+2y+4=4 \Leftrightarrow (x-2)(y-2)=4.$$ Note that $4=2 \cdot 2$ or $4=4 \cdot 1=1 \cdot 4$, the case $x-2=y-2=2$ leads to $x=y=4$, an that contradicts the hipótesis. The case $x-2=4$ and $y-2=1$ leads to $x=6$ and $y=3$ (the other case, $x-2=1$ and $y-2=4$ leads to a similar case). Finally, since $(-2)(-2)=(-4)(-1)=(-1)(-4)=4$, the cases $4=(-1)(-4)=(-4)(-1)$ leads to   $x=-2$ or $y=-2$, respectively. Finally, the case $(-2)(-2)=4$ gives us $x=y=0$, another contradiction. 
So the answer is $(x,y)=(6,3)$ or $(x,y)=(3,6)$, and indeed $A=6\cdot 3=18=2 \cdot 6 + 2\cdot 3=P$.
