What is the maximum number of nonoverlapping squares with sides of length 3 that will fit inside of a square with sides of length 6?
Draw a diagram of this problem. How many squares fit into the larger square?
To find the maximum number of non-overlapping squares with sides of length 3 that will fit inside a larger square with sides of length 6, we can start by calculating the area of the smaller square.
The area of each individual square with sides of length 3 is \(3 \times 3 = 9\) square units.
Next, we calculate the area of the larger square. The area of a square is given by the formula \(side \times side\), so for a square with sides of length 6, the area is \(6 \times 6 = 36\) square units.
Now, we divide the area of the larger square by the area of each individual square to determine the maximum number of squares that can fit inside.
\(36 \, \text{square units} \div 9 \, \text{square units per square} = 4\) squares.
Therefore, the maximum number of non-overlapping squares with sides of length 3 that will fit inside a larger square with sides of length 6 is 4.