The areas of two squares are in the ratio $25:36$. What is the ratio of their perimeters? Express your answer in the form $a:b$.
Let's call the first square's side length w and the second square's side length x. And let's call the side length of the second square y. Therefore, the area of the first square is $x^2$ and the area of the second square is $y^2$. We can set up ratios with these areas. $x^2:y^2=25:36$. Now we need to find the ratio of their perimeters. The perimeter of a square is just 4 times its side length. So the perimeter of the first square is 4x and the perimeter of the second square is 4y. Therefore, the ratio of their perimeters is $4x:4y$. But since we know that $x^2:y^2=25:36$, we can say that x:y=5:6. Right. So $4x:4y$ is equal to $4*5:4*6$. Which simplifies to $20:24$. But we need to find the greatest common factor of 20 and 24. Which is 4. So our final answer is $5:6$.

