the area of a quadrilateral is 200 square feet and its longest side is 20 feet long. find the length of the longest side of a similar polygon whose area is 400 square feet.
the area is proportional to the square of the side length
200 / (20^2) = 400 / L^2
50
28.28
To find the length of the longest side of a similar polygon with an area of 400 square feet, we can use the concept of ratios.
Given that the area of the first quadrilateral is 200 square feet, we need to find the scale factor between the two polygons.
The scale factor, denoted as k, can be found by taking the square root of the ratio of the areas. In this case, the scale factor k is √(400/200) = √2.
Since the longest side of the first quadrilateral is 20 feet, we can find the length of the longest side of the similar polygon by multiplying the length of the longest side of the first quadrilateral by the scale factor.
Length of longest side of the similar polygon = 20 feet * √2 = 20√2 feet.
Therefore, the length of the longest side of the similar polygon with an area of 400 square feet is 20√2 feet.