30: 1x30, 2x15, 3x10, 5x6
24: 1x24, 2x12, 3x8, 4x6
36: 1x36, 2x18, 3x12, 4x9 (6x6 is not a rectangle).
17: 1x17
3
There are an infinite number of rectangles with this perimeter. The "whole number" sides could be (5 x 1), (4 x 2) or (3 x 3), but (5½ x ½) or (3¼ x 2¾) etc would fit the description.
You can't tell the dimensions from the perimeter. There are an infinite number of different rectangles, all with different lengths and widths, that all have the same perimeter.
Each rectangle has four sides. Therefore, for four rectangles, you would multiply the number of rectangles by the number of sides per rectangle: 4 rectangles × 4 sides/rectangle = 16 sides. Thus, the total number of sides of four rectangles is 16.
There are infinitely many such rectangles.
3
There would be an infinite number of rectangles possible
If you can compile a complete list of all different rectangular models with sides of integer length for a number then their lengths and breadths represent its factors.
No, not every possible minimal spanning tree of a given graph has an identical number of edges.
5
There are an infinite number of rectangles with this perimeter. The "whole number" sides could be (5 x 1), (4 x 2) or (3 x 3), but (5½ x ½) or (3¼ x 2¾) etc would fit the description.
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.
You can't. There are an infinite number of possible rectangles with a given area.
You can't tell the dimensions from the perimeter. There are an infinite number of different rectangles, all with different lengths and widths, that all have the same perimeter.
There is no relationship between the perimeter and area of a rectangle. Knowing the perimeter, it's not possible to find the area. If you pick a number for the perimeter, there are an infinite number of rectangles with different areas that all have that perimeter. Knowing the area, it's not possible to find the perimeter. If you pick a number for the area, there are an infinite number of rectangles with different perimeters that all have that area.
To determine the number of rectangles that can be made using 24 tiles, we need to consider the different possible dimensions of rectangles. A rectangle can have a length and width ranging from 1 to 24, inclusive. Each unique combination of length and width will form a distinct rectangle, so the total number of rectangles can be calculated by summing the total number of combinations for each possible length and width. This can be done using the formula n(n+1)/2 for the sum of the first n natural numbers, where n is the total number of tiles (24 in this case).
No.