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A person plans to cut three pieces from a single board measuring 91 cm in total length. Let the shortest piece have length x cm. The second piece is 3 cm longer than the shortest piece, and the third piece is twice the length of the shortest piece. If the third piece is at least 5 cm longer than the second piece, which of the following gives the possible length of the shortest piece?

1. less than 8 cm
2. greater than or equal to 8 cm but less than or equal to 22 cm
3. less than 22 cm
4. greater than 22 cm

Correct answer: greater than or equal to 8 cm but less than or equal to 22 cm

Solution

The correct option is right because the conditions set by the problem require that the total length of the pieces, which are defined in terms of the shortest piece x, must not exceed 91 cm. Additionally, the requirement that the third piece is at least 5 cm longer than the second piece establishes a lower limit for x, while the total length constraint establishes an upper limit, resulting in the range of x being from 8 cm to 22 cm.

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