the ratio of the areas of two squares is 9:4. the ratio of their perimeters is
(please explain in detail)
To find the ratio of the perimeters of two squares, we need to understand the relationship between the areas and perimeters of squares.
First, let's define the formula for calculating the area and perimeter of a square:
Area of a square = side length × side length = (s^2)
Perimeter of a square = 4 × side length = (4s)
Now, let's assume we have two squares with side lengths of "x" and "y" respectively.
Given that the ratio of their areas is 9:4, we can write the equation as:
(area of the first square) / (area of the second square) = 9/4
This can be expressed as:
(x^2) / (y^2) = 9/4
Now, let's solve for the ratio of their perimeters.
The perimeter of the first square is (4x) and the perimeter of the second square is (4y), so the equation becomes:
(perimeter of the first square) / (perimeter of the second square) = (4x) / (4y)
We can simplify this further by canceling out the common factor of 4:
(perimeter of the first square) / (perimeter of the second square) = x / y
So, the ratio of the perimeters of the two squares is x:y.
Therefore, the ratio of their perimeters is equal to the ratio of their side lengths.
In summary, if the ratio of the areas of two squares is 9:4, then the ratio of their perimeters is x:y, where "x" and "y" are the side lengths of the squares.
To find the ratio of the perimeters of two squares when given the ratio of their areas, we need to understand the relationship between the sides, areas, and perimeters of squares.
Let's assume the side length of the first square is 'x'. Therefore, the area of the first square would be x^2, and the perimeter would be 4x (since each side of a square is equal in length).
Now, let's assume the side length of the second square is 'y'. The area of the second square would be y^2, and the perimeter would be 4y.
We know that the ratio of the areas of the two squares is given as 9:4. Therefore, we can set up the equation:
x^2 : y^2 = 9 : 4
To simplify this, we can take the square root of both sides:
√(x^2) : √(y^2) = √9 : √4
Simplifying further, we get:
x : y = 3 : 2
Now, we have the ratio of the side lengths of the squares, which means the ratio of their perimeters will be the same.
Therefore, the ratio of the perimeters of the two squares is 3 : 2.