### Instruction: The areas of two squares are in the ratio $25:36$. What is the ratio of their perimeters? Express your answer in the form $a:b$.### Response: To find the ratio of the perimeters of two squares, I need to find the ratio of their side lengths first.
If the areas of the squares are in the ratio $25:36$, then the ratio of their side lengths is the square root of that ratio, since $A = s^2$ for a square with side length $s$ and area $A$.
So the ratio of the side lengths is $\sqrt{25}:\sqrt{36}$, which simplifies to $5:6$.
Now, the perimeter of a square is four times its side length, so the ratio of the perimeters is also four times the ratio of the side lengths.
Therefore, the ratio of the perimeters is $(4\times 5):(4\times 6)$, which simplifies to $20:24$.