Question

Nimerah is painting one wall of her room with a pattern of squares. She wants to alternate between red squares with an area of 9 square inches and blue squares with an area of 4 square inches (Area of a square = s²).

Part A: Find the side length of each square. Show or explain your work.

Part B: If she has enough room to place 6 of each type of square with no space between them, how long is the wall?

Answer 1

The red squares have a side length of 3 inches each, and the blue squares have a side length of 2 inches each. For the wall, there are 6 of each type of square, resulting in a total wall length of 30 inches.

Step-by-step explanation:

The student is asking about the side lengths of red and blue squares, and the total length of a wall that Nimerah wants to paint with these squares.

Part A: Side Length of Each Square

For the red square with an area of 9 square inches, its side length can be found using the formula for the area of a square A = s². We take the square root of the area to find the side length:

Side length of red square = √(9 square inches) = 3 inches.
Similarly, for the blue square with an area of 4 square inches, the process is the same:

Side length of blue square = √(4 square inches) = 2 inches.

Part B: Total Length of the Wall

Since there will be 6 red squares and 6 blue squares placed next to each other, we need to add up the individual lengths of the squares. The red squares have a side length of 3 inches each and the blue squares have a side length of 2 inches each, so the total length of the wall will be:

Total length = (6 x 3 inches) + (6 x 2 inches) = 18 inches + 12 inches = 30 inches.