The areas are many. If you have 36 feet of fence you can make a rectangle 8' x 10' x 8' x 10'. That rectangle would be 80 square feet. 8 x 10 = 80 9 x 9 x 9 x 9 would be 81 square feet. 9 x 9 = 81 12 x 6 x 12 x 6 would be 72 square feet. 12 x 6 = 72 3 x 15 x 3 x 15 would be 45 square feet. 3 x 15 = 45 All the sides of each rectangle add up to 36 which is the length of fence that you had. You could make one 1 x 17 x 1 x 17 which would be 17 square feet. 1 x 17 = 17 17 (17x17x1x1) 32 (16x16x2x2) 45 (15x15x3x3) 56 (14x14x4x4) 65 (13x13x5x5) 72 (12x12x6x6) 77 (11x11x7x7) 80 (10x10x8x8) 81 (9x9x9x9) [a square is, in a way, a rectangle that's gotten its act together]
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It's very easy for two rectangles to have the same area and different perimeters,or the same perimeter and different areas. In either case, it would be obvious toyou when you see them that there's something different about them, and theywould not fit one on top of the other.But if two rectangles have the same area and the same perimeter, then to look at themyou'd swear that they're the same rectangle, and one could be laid down on the otherand fit exactly.
An L-shaped area can be divided into two rectangles. The total area is the sum of the areas of the two rectangles.
You can't tell the linear dimensions from knowing only the area. There are an infinite number of shapes that all have the same area. Even if you consider only rectangles, there are still an infinite number of different rectangles, all with different lengths and widths, that all have areas of 5,000 acres.
The ratio of their perimeters is also 45/35 = 9/7. The ratio of their areas is (9/7)2 = 81/63
In order to get a rectangle with an area of 24 centimeters, the length and width multiplied need to equal 24. On top of that, length and width may not be equal, or the shape would be a square instead of a rectangle. Examples of rectangles with 24cm areas: 1x24 cm 2x12 cm 3x8 cm 4x6 cm