Final answer:
The longest item that could fit in Jasmine's pencil tin is approximately 18.37 cm, calculated using the Pythagorean theorem. Jasmine's stylus, which is 17.6 cm long, could fit diagonally, but practical issues with clearance may prevent it from fitting properly.
Step-by-step explanation:
To determine the length of the longest item that could fit in the pencil tin, we must consider the diagonal of the tin. This is because even though the stylus is longer than one dimension of the tin, it might fit diagonally if the diagonal is longer than the stylus. To find the diagonal inside the tin, we use the Pythagorean theorem in three dimensions.
First, calculate the square of the lengths of all sides:
- 17.1 cm × 17.1 cm = 292.41 cm²
- 6 cm × 6 cm = 36 cm²
- 3 cm × 3 cm = 9 cm²
Then add them together:
292.41 cm² + 36 cm² + 9 cm² = 337.41 cm²
Now take the square root:
√337.41 cm² = 18.37 cm
The longest item that could fit in the pencil tin is approximately 18.37 cm long. Therefore, despite Jasmine's concern, the stylus which is 17.6 cm long could theoretically fit in her pencil tin diagonally.
However, the stylus might not fit if there is not enough clearance at the corners or if the tin's lid does not close due to the stylus's thickness.