### 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: Let's have the side of the first square be $x$.
And the side of the second square be $y$.
So the area of the first square would be $x^2$.
And the area of the second square would be $y^2$.
And the ratio of their areas would be $x^2 / y^2$ which is 25/36. So $x^2 / y^2 = 25/36$.
Now let's turn to the perimeters. The perimeter of the first square would be $4x$.
And the perimeter of the second square would be $4y$.
So the ratio of their perimeters would be $4x / 4y$ which is $x/y$.
And we already figured out that $x^2 / y^2 = 25/36$.
So $x/y = \sqrt{25/36}$ which is $5/6$.