Answer :
Final answer:
Mrs. Carter can create six distinct rectangles using the 18 square boxes of tacks by arranging them in configurations based on the factors of 18: 18x1, 9x2, 6x3, 3x6, 2x9, and 1x18.
Explanation:
Mrs. Carter can make different rectangles with the 18 square boxes of tacks based on the number of total boxes and their possible arrangements. First, consider the factors of 18, as each pair of factors will represent one possible rectangle. The factors of 18 are 1, 2, 3, 6, 9, and 18.
Thus, she could form:
- One rectangle with dimensions of 18x1 (18 boxes, each one row tall),
- One rectangle with dimensions of 9x2 (9 pairs of boxes stacked two high),
- One rectangle with dimensions of 6x3 (six sets of boxes stacked three high),
- One rectangle with dimensions of 3x6 (three sets of boxes stacked six high),
- One rectangle with dimensions of 2x9 (two sets of boxes stacked nine high), and
- One rectangle with dimensions of 1x18 (one row of 18 boxes).
So, in total, Mrs. Carter can create six different rectangles from 18 square boxes of tacks.
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