Final Answer:
The largest distance x before both boards topple over is C) 14 cm.
Step-by-step explanation:
To determine the maximum overhang distance x before the boards topple, consider the combined center of mass. The first board's center of mass is at 15 cm (half of its length), while the second board's center of mass coincides with the first board's edge. The system topples when the combined center of mass crosses the support point (table edge).(C)
For the boards not to topple, the center of mass of the combined system must stay within the width of the lower board. With an overhang of 8 cm, the combined center of mass is at 23 cm from the edge of the table (15 cm + 8 cm).
Since the maximum stable overhang occurs when the combined center of mass is at the edge, the maximum allowable x is 23 cm (combined center of mass) minus 9 cm (half the length of one board) equals 14 cm.
Therefore, to prevent the boards from toppling over, x should not exceed 14 cm. Beyond this point, the combined center of mass extends beyond the support provided by the lower board, causing instability and potential toppling.
This analysis ensures stability by considering the distribution of mass and the center of gravity to determine the maximum permissible overhang distance x before the boards topple over due to an imbalance in the system.