Final answer:
The question assumes the board is square, but with an area of 874 square inches, none of the given lengths (27, 29, 31, 33 inches) when squared result in 874. Additional information or clarification on the shape of the board is needed to provide an accurate answer.
Step-by-step explanation:
The student is tasked with finding the length of a side of a flat board with an area of 874 square inches where the length is a whole number. This problem falls under the Mathematics category and involves understanding area and dimension calculations. In this case, we need to find a whole number that, when squared (since the sides of a board are typically the same length in a square shape), equals 874.
- Start by looking for pairs of factors that multiply together to give you the area of 874.
- Calculate the square root of 874 to narrow down the possible whole number length.
- The exact square root of 874 is not a whole number, but finding the nearest whole numbers will provide possible side lengths.
- Upon performing the calculation or checking a list of perfect squares, it is found that none of the given options (27, 29, 31, 33) are squares of 874.
Therefore, the assumption that the board must be square is incorrect. The board may be rectangular, and so the question cannot be answered without additional information about either the width of the board or assuming that it is square. We must clarify the shape of the board to provide a specific answer.