To determine how many smaller right triangles with side lengths of \(5\sqrt{3}\) centimeters fit along the longer side of the large right triangle with side length \(40\sqrt{12}\) centimeters, we need to first identify the longer side of the larger triangle and then divide it by the length of the smaller triangles.
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Calculate the long side of the large triangle:
- The side length of the large triangle is given as \(40\sqrt{12}\) centimeters.
- We can simplify this: \[ \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \] Thus, \[ 40\sqrt{12} = 40 \times 2\sqrt{3} = 80\sqrt{3} \]
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Determine how many smaller triangles fit along this length:
- Each smaller triangle has a side length of \(5\sqrt{3}\).
- We need to divide the length of the large triangle by the length of a smaller triangle: \[ \text{Number of smaller triangles} = \frac{80\sqrt{3}}{5\sqrt{3}} \]
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Simplify the division:
- The \(\sqrt{3}\) terms cancel out: \[ \frac{80\sqrt{3}}{5\sqrt{3}} = \frac{80}{5} = 16 \]
Therefore, the number of smaller triangles that can fit along the longer side of the larger triangle is \(\boxed{16}\).