using only whole numbers how can you draw three rectangles with a perimeter of 12 units?
5L,1W
3L,3W
4L,2W
5+5+1+1 4+4+2+2
how many different triangles can you make with perimeter of 12units?
To draw three rectangles with a perimeter of 12 units using only whole numbers, we need to distribute the 12 units amongst the lengths and widths of the rectangles. Let's break it down step by step:
1. First, determine the range of whole number values for the sides of the rectangles.
Since we are working with whole numbers, the minimum value of each side can be 1. As for the maximum value, let's consider the situation where all three rectangles have a side length of 3 (which is the minimum value needed to form a rectangle). In this case, the perimeter would be:
Perimeter = 3 + 3 + 3 = 9 units.
Note that using a side length greater than 3 would result in an even smaller perimeter, so 3 is the maximum value we can use.
2. Divide the 12 units of perimeter amongst the three rectangles.
Since we already established that each rectangle's maximum side length can be 3 units, the biggest possible perimeter for each rectangle would be 2 x (3 + 3) = 12 units.
Therefore, we can distribute the 12 units of perimeter evenly among the three rectangles by giving each rectangle a perimeter of 4 units.
3. Find the different combinations of side lengths for the rectangles that result in a perimeter of 4 units.
Let's list all the possible combinations of side lengths for rectangles with a perimeter of 4 units:
Rectangles: Side lengths
1st rectangle: 1 x 1
2nd rectangle: 2 x 0
3rd rectangle: 0 x 2
The first rectangle could have dimensions of 1 unit by 1 unit, which sums up to a perimeter of 4 units.
Alternatively, the second and third rectangles could have one side equal to 2 units and the other side equal to 0 units. Although visually these rectangles would not appear as rectangles, mathematically they still meet the definition of a rectangle and have a perimeter of 4 units.
So, using whole numbers, we can draw three rectangles with a perimeter of 12 units with the following side lengths:
1st rectangle: 1 unit x 1 unit
2nd rectangle: 2 units x 0 units (or flipped – 0 units x 2 units)
3rd rectangle: 0 units x 2 units (or flipped – 2 units x 0 units)