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What happens to the area when you interchange the length and width? For example, compare the areas of a rectangle of length 11 meters and width 14 meters with a rectangle of length 14 meters and width 11 meters. What patterns would you notice if you were to plot more length and area pairs on the graph
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Guest User
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Mahesh Godavarti
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The area of a rectangle is given by length x width.


Therefore, if the length and width are interchanged the area remains constant.


If we plot more length and area pairs (while keeping the perimeter constant = 25 meters), we will notice that the points form an inverted parabola.



Sangeetha Pulapaka
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https://im.kendallhunt.com/HS/students/1/6/1/index.html




1. The area stays the same if the length and width are interchanged because the area is the product of the length and the width.

2. Many of the areas would come with two different pairs: for example, 100 comes from the pair (5,100) but also from the pair (20,100) because a rectangle with length 5 meters and width 20 meters is the same as a rectangle with length 20 meters and width 5 meters. Using a different length and corresponding width, the 156 comes from the pair and also from the pair (12,156) and also from the pair (13,156). The points on the graph would have reflectional symmetry about the line x = 12.5.