a preschool has a rectangular field and a rectangular playground, that are similar in shape. each dimension of the field is 3.2 times the corresponding dimension of the playground
You did not state a question.
If the question is what is the ratio of the field areas it is
area field = 3.2^2 * area playground
3.2^2 = 10.24
yeah
To find the dimensions of the field and the playground, we can set up a system of equations using the given information.
Let's assume the length of the playground is x. Since the field is 3.2 times the corresponding dimension of the playground, the length of the field would be 3.2x.
Similarly, let's assume the width of the playground is y. Therefore, the width of the field would be 3.2y.
So, we have the following equations:
Length of the field = 3.2 times length of the playground
Width of the field = 3.2 times width of the playground
Equation 1: 3.2x = length of the field
Equation 2: 3.2y = width of the field
These two equations represent the relationship between the dimensions of the field and the playground.
With these equations, we can solve for the dimensions. If you know the values of x and y (length and width of the playground), you can substitute them into the equations to find the corresponding dimensions of the field.
For example, if the length of the playground, x, is 10 meters, then the length of the field would be 3.2 times 10, which is 32 meters. Similarly, if the width of the playground, y, is 5 meters, then the width of the field would be 3.2 times 5, which is 16 meters.
Remember, the ratio between the dimensions of the field and the playground remains constant at 3.2. This means that no matter what values you choose for x and y, the ratio between their corresponding dimensions will always be 3.2.