Question

1. maria made an arrangement of these blocks in a rectangular shape. she wants to explore other unique arrangements she can make with the same number of blocks. record the dimensions of other arrangements maria could make.

Explanation:

Step1: Find factor - pairs

We need to find all factor - pairs of the number of blocks. Let's assume the number of blocks is not given in the visible part, but if we consider the concept of arranging blocks into rectangles, we are looking for pairs of positive integers \(a\) and \(b\) such that the total number of blocks \(n=a\times b\). For example, if \(n = 12\), the factor - pairs are \((1,12)\), \((2,6)\), and \((3,4)\) which correspond to rectangles with dimensions \(1\times12\), \(2\times6\), and \(3\times4\).

Step2: List dimensions

For each factor - pair \((a,b)\), the dimensions of the rectangle are \(a\) by \(b\) (and \(b\) by \(a\) which we consider the same rectangle for non - oriented cases). If we assume the number of blocks is \(18\) (from the partial text "Tom has 18 stickers" which might be related to the number of blocks), the factor - pairs of 18 are \((1,18)\) with dimensions \(1\times18\), \((2,9)\) with dimensions \(2\times9\), and \((3,6)\) with dimensions \(3\times6\).

Answer:

If the number of blocks is 18, the possible dimensions of rectangles are \(1\times18\), \(2\times9\), \(3\times6\)