Given:
Side length of square is x = 10 in.
To find:
Area of a square with side length x when x = 10 in.
Check whether the area of a square and the length of its side directly proportional.
Solution:
Area of square is
[tex]Area=(side)^2[/tex]
[tex]Area=x^2[/tex]
For x=10, we have
[tex]Area=(10)^2[/tex]
[tex]Area=100[/tex]
Therefore, the area of square is 100 sq. in. when x=10 in.
For x=1,
[tex]A_1=1^2=1[/tex]
[tex]\dfrac{A_1}{x_1}=\dfrac{1}{1}=1[/tex]
For x=2,
[tex]A_2=1^2=4[/tex]
[tex]\dfrac{A_2}{x_2}=\dfrac{4}{2}=2[/tex]
Here, [tex]\dfrac{A_1}{x_1}\neq \dfrac{A_2}{x_2}[/tex].
Since, [tex]Area=(side)^2[/tex] and ratio of area and sides are not always same, therefore the area of depends on the side but not directly proportional to its side.
