Two similar polygons have areas of 50 and 100 sq. in. What is the ratio of the length of a pair of corresponding sides?

how would you write it with the root on top divided by another number?

According to what I told you in the previous post

50/100 = (x1)^2 / (x2)^2
1/2 = (x1)^2 / (x2)^2

x1 : x2 = 1 : √2

To find the ratio of the length of a pair of corresponding sides, we need to find the square root of the ratio of the areas.

Let's call the length of the corresponding sides of the polygons x.

The ratio of the areas is given by (Area of larger polygon)/(Area of smaller polygon).

In this case, the areas are 100 sq. in. and 50 sq. in., so the ratio of the areas is 100/50 = 2.

Taking the square root of the ratio of the areas, we get √2.

Therefore, the ratio of the length of a pair of corresponding sides is √2 : 1.

To find the ratio of the length of corresponding sides, we need to compare the areas of the two similar polygons. The relationship between the areas of two similar polygons is given by the square of the ratio of their corresponding sides.

Let's assume that the ratio of the length of a pair of corresponding sides is x:1. Then, the ratio of the areas of the two polygons can be expressed as x^2:1 (since area is a two-dimensional concept).

Given that the area of one polygon is 50 sq. in. and the other polygon is 100 sq. in., we can set up the following equation:

x^2:1 = 50:100

We can simplify the right side of the equation by dividing both numbers by 50:

x^2:1 = 1:2

Now, we can cross-multiply the ratio:

x^2 * 2 = 1 * 1

2x^2 = 1

To isolate x, we can divide both sides of the equation by 2:

x^2 = 1/2

Taking the square root of both sides:

x = √(1/2)

So, the ratio of the length of a pair of corresponding sides is √(1/2) : 1.