the areas of two similar rectangles are 338 cm squared and 73 cm squared. what is the similarity ratio of the perimeters
√338 : √73
To find the similarity ratio of the perimeters of two similar rectangles, we need to find the ratio of any two corresponding sides of the rectangles.
Given that the areas of the rectangles are 338 cm² and 73 cm², let's assume the lengths of their corresponding sides are x and y, respectively.
The formula for the area of a rectangle is A = length × width. Therefore, we can set up the following equations:
x * width1 = 338 (Equation 1)
y * width2 = 73 (Equation 2)
To find the similarity ratio of the perimeters, we need to find the ratio between the perimeter of the first rectangle (2x + 2*width1) and the perimeter of the second rectangle (2y + 2*width2).
Now, let's solve the equations to find the values of x and y:
From Equation 1: x * width1 = 338
We can rearrange this equation to express width1 in terms of x:
width1 = 338 / x
Similarly, from Equation 2: y * width2 = 73
Rearranging this equation, we have:
width2 = 73 / y
Now, we substitute these expressions for width1 and width2 into the perimeter formula:
Perimeter of the first rectangle = 2x + 2 * (338 / x)
Perimeter of the second rectangle = 2y + 2 * (73 / y)
The similarity ratio of the perimeters is the ratio of these two values:
Ratio = (2x + 2 * (338 / x)) / (2y + 2 * (73 / y))
Simplifying the expression further:
Ratio = (2(x^2) + 676) / (2(y^2) + 146)
Hence, the similarity ratio of the perimeters is (2(x^2) + 676) / (2(y^2) + 146).