To determine how many whole square pieces of cake can be cut from a rectangular cake, we need to know the dimensions of the cake (length and width) and the side length of the square pieces.
Let's denote:
- Length of the cake: \( L \) inches
- Width of the cake: \( W \) inches
- Side length of the square pieces: \( S \) inches
The total area of the rectangular cake is \( L \times W \) square inches. The area of one square piece is \( S \times S = S^2 \) square inches.
To find out how many whole square pieces can be cut from the cake, we need to calculate how many squares fit along the length and width of the rectangular cake:
- The number of squares that fit along the length (\( N_L \)) is given by \( N_L = \left\lfloor \frac{L}{S} \right\rfloor \).
- The number of squares that fit along the width (\( N_W \)) is given by \( N_W = \left\lfloor \frac{W}{S} \right\rfloor \).
The total number of square pieces of cake is then the product of these two values: \[ N = N_L \times N_W = \left\lfloor \frac{L}{S} \right\rfloor \times \left\lfloor \frac{W}{S} \right\rfloor \]
Since the specific values for \( L \), \( W \), and \( S \) are not provided, the exact calculation cannot be performed.
If you have specific values for the length, width, and side lengths, please provide them so that we can compute the exact number of square pieces of cake. Otherwise, based on the options you provided (55, 54, 53, 56), I cannot determine a correct answer without more information.
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