Question

common core assessment 18. gayle made a baby quilt using 24 equal squares. she wants to know the side length of one square. part a describe one way to find the answer. part b what is the side length of one square? write an equation to show your work. (image of a quilt with dimensions 3 ft and 4.5 ft, and 24 equal squares with red hearts on some of them)

Explanation:

Part A

Step1: Determine quilt's area

The quilt is a rectangle with length \( 4.5 \) ft and width \( 3 \) ft. The area of a rectangle is \( A = l \times w \), so \( A = 4.5 \times 3 \).

Step2: Divide area by number of squares

There are 24 equal squares. To find the area of one square, divide the total area by 24. Then, take the square root of that area to find the side length (since the area of a square is \( s^2 \), so \( s=\sqrt{\text{area of one square}} \)).

Part B

Step1: Calculate total area of quilt

The quilt is a rectangle with length \( l = 4.5 \) ft and width \( w = 3 \) ft. The area of a rectangle is given by the formula \( A = l\times w \). So, \( A = 4.5\times3 = 13.5 \) square feet.

Step2: Find area of one square

There are 24 equal squares, so the area of one square (\( A_{square} \)) is the total area divided by 24. So, \( A_{square}=\frac{13.5}{24} = 0.5625 \) square feet.

Step3: Find side length of one square

Let the side length of one square be \( s \). The area of a square is \( A = s^2 \). So, to find \( s \), we take the square root of the area of one square. \( s=\sqrt{0.5625} = 0.75 \) feet. We can also set up the equation from the start: Let \( s \) be the side length of one square. The total area of 24 squares is \( 24s^2 \), and this equals the area of the quilt (\( 4.5\times3 \)). So the equation is \( 24s^2=4.5\times3 \). Solving for \( s \):
First, calculate \( 4.5\times3 = 13.5 \). Then, \( 24s^2 = 13.5 \). Divide both sides by 24: \( s^2=\frac{13.5}{24}=0.5625 \). Then take the square root: \( s = \sqrt{0.5625}=0.75 \).

Answer:

(Part A):
One way is to first find the area of the quilt (length × width = 4.5×3), then divide that area by 24 to get the area of one square, and finally take the square root of that area to find the side length.