The area of an integer-sided rectangle is $20$. What is the minimum possible value of its perimeter?

Step 1: Let the integer side lengths of the rectangle be $l$ and $b$. The area is:

Step 2: The perimeter $P$ is given by $2(l+b)$. The possible factor pairs $(l,b)$ of $20$ are:

• $(1,20)⟹P=2(1+20)=42$

• $(2,10)⟹P=2(2+10)=24$

• $(4,5)⟹P=2(4+5)=18$

Step 3: The minimum perimeter is therefore $18$, which occurs when the sides are closest to each other (approaching a square).