James has some square paving stones and some rectangular paving stones. He uses four square paving stones and six rectangular paving stones to make this pattern in the shape of a rectangle. Each rectangular paving stone is 60 mathrm(cm) by 30 mathrm(~cm) . Work out the length of one side of a square paving stone. (2 marks)

## Step 1: <br />Firstly, we need to understand the problem. James uses four square paving stones and six rectangular paving stones to form a rectangle. The dimensions of the rectangular paving stones are given, but we need to find the length of one side of the square paving stone.<br /><br />## Step 2: <br />We know that the total width of the rectangle is equal to the side length of the square paving stone, because the square paving stones are placed along the width of the rectangle.<br /><br />## Step 3: <br />The total length of the rectangle is made up of the lengths of two rectangular paving stones. Since each rectangular paving stone is 60 cm long, the total length of the rectangle is \(2 \times 60 = 120\) cm.<br /><br />## Step 4: <br />Since the rectangle is made up of the square and rectangular paving stones, the length of the rectangle is also equal to the total length of three square paving stones and three rectangular paving stones placed side by side.<br /><br />### \(120 = 3 \times \text{Side length of square} + 3 \times 30\)<br /><br />## Step 5: <br />We can simplify the equation by dividing through by 3.<br /><br />### \(40 = \text{Side length of square} + 30\)<br /><br />## Step 6: <br />Finally, we can solve for the side length of the square by subtracting 30 from both sides of the equation.<br /><br />### \(\text{Side length of square} = 40 - 30\)