Two similar polygons have areas of 50 and 100 sq. in. Find the ratio of the length of a pair of corresponding sides.
area is 1:2
sides are thus 1:√2
To find the ratio of the length of a pair of corresponding sides of two similar polygons, you need to take the square root of the ratio of their areas.
Step 1: Calculate the square root of the ratio of the areas.
In this case, the ratio of the areas is 100/50 = 2. Taking the square root of 2 gives us √2.
Step 2: Use the square root of the area ratio to find the ratio of the corresponding sides.
The ratio of the length of a pair of corresponding sides is simply the square root of the ratio of the areas. Therefore, the ratio of the length of a pair of corresponding sides is √2.
So, the ratio of the length of a pair of corresponding sides is √2 or approximately 1.414.