Answer:
1) 120 units
2) see attachment
Step-by-step explanation:
Given a figure composed of 21 squares that each have an area of 25 square units, you want to know (1) the perimeter of the figure, and (2) how to rearrange it to have the same perimeter, but with sides that line up.
(1) Perimeter
The perimeter is the sum of the lengths of the sides that form the boundary of the figure. The boundary consists of ...
- 6 top-side horizontal edges
- 6 bottom-side horizontal edges
- 6 left-side vertical edges
- 6 right-side vertical edges
for a total of 6·4 = 24 edges of the squares shown.
Each of the squares shown has an area of A = s² = 25 units², so a side length of s = √(25 units²) = 5 units.
The perimeter is the length of 24 of these edges, so is ...
perimeter = 24 × 5 units = 120 units
(2) Rearrangement
The 21 squares shown in the figure can only be rearranged into rectangles that are 21 × 1 squares or 7 × 3 squares. These will have perimeters of 44 or 20 edges, respectively. Hence, it is not possible to have "sides of the squares line up" in a rectangle with the same perimeter.
The attached figure is the next best thing. It shows a 6 × 4 rectangle with three squares removed (to keep the total at 21). The number of horizontal and vertical edges total 24, as required to keep the same perimeter.
