Question

part a
fill in the table for side length and area of different squares.

side length (cm)	area (cm²)
100
25
s	²

part b
is the relationship between the side length of a square and the area of a square proportional? select choice

Explanation:

Step1: Recall the formula for the area of a square

The area \( A \) of a square with side length \( s \) is given by the formula \( A = s^2 \).

Step2: Calculate the area for side length 3 cm

Substitute \( s = 3 \) into the formula: \( A = 3^2 = 9 \).

Step3: Calculate the area for side length 100 cm

Substitute \( s = 100 \) into the formula: \( A = 100^2 = 10000 \).

Step4: Calculate the area for side length 25 cm

Substitute \( s = 25 \) into the formula: \( A = 25^2 = 625 \).

Step5: Determine the general formula for side length \( s \)

Using the area formula for a square, the area when the side length is \( s \) is \( s^2 \), so the box should be filled with \( s \) (since the exponent 2 is already given outside the box).

Step6: Analyze proportionality (Part B)

For a relationship to be proportional, it should be of the form \( y = kx \) where \( k \) is a constant. The area of a square is \( A = s^2 \), which is a quadratic relationship, not a linear one (since the exponent of \( s \) is 2, not 1). So the relationship between side length and area is not proportional.

Answer:

(Part A Table):

Side Length (cm)	Area (cm²)
100	10000
25	625
\( s \)	\( s \)	(with the \( ^2 \) outside the box as given)