Question

lesson 4 cool down
answer all the questions to the best of your ability. be sure to show all work.

1. complete the table with the perimeter of a square for each given side length.
2. write a rule for a function, p, that gives the perimeter of a square in inches when the side length is x inches.
3. what is the value of p(9.1)? what does it tell us about the side length and perimeter of the square?

side length (inches)	perimeter (inches)
7
20
x

Explanation:

Step1: Recall the formula for the perimeter of a square

The perimeter \( P \) of a square with side length \( s \) is given by \( P = 4s \), since a square has 4 equal sides.

Step2: Complete the table for each side length

• For side length \( 0.5 \) inches:

Using the formula \( P = 4s \), substitute \( s = 0.5 \). So \( P = 4\times0.5 = 2 \) inches.

• For side length \( 7 \) inches:

Substitute \( s = 7 \) into \( P = 4s \). Then \( P = 4\times7 = 28 \) inches.

• For side length \( 20 \) inches:

Substitute \( s = 20 \) into \( P = 4s \). We get \( P = 4\times20 = 80 \) inches.

• For side length \( x \) inches:

Using the formula, the perimeter \( P = 4x \) inches.

Step3: Write the function rule

From the perimeter formula of a square, the function \( P \) that gives the perimeter when the side length is \( x \) inches is \( P(x)=4x \).

Step4: Find \( P(9.1) \)

Substitute \( x = 9.1 \) into the function \( P(x)=4x \). So \( P(9.1)=4\times9.1 = 36.4 \). This tells us that when the side length of the square is \( 9.1 \) inches, the perimeter of the square is \( 36.4 \) inches.

Answer:

(for the table completion):

Side length (inches)	Perimeter (inches)
\( 7 \)	\( 28 \)
\( 20 \)	\( 80 \)
\( x \)	\( 4x \)