how many rectangles can have the perimiter of 46m
P = 2 W + 2 L
P = 2 ( W + L )
46 = 2 ( W + L ) Divide both sides by 2
46 / 2 ) = 2 ( W + L ) / 2
23 = W + L
W + L = 23
For integers :
W = 1 m
L = 22 m
W = 2 m
L = 21 m
W = 3 m
L = 20 m
etc.
math
To determine the number of rectangles possible with a perimeter of 46m, we need to consider the different combinations of side lengths. The perimeter of a rectangle is calculated by adding together the lengths of all four sides.
Let's start by listing all possible side lengths that can be used:
1m, 2m, 3m, 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m, 15m, 16m, 17m, 18m, 19m, 20m, 21m, 22m, 23m, 24m, 25m
Now, we'll try to form rectangles using these side lengths that have a perimeter of 46m. To do this, we can systematically combine different lengths to find valid rectangles.
For example, we can try combining side lengths of 1m and 22m to form a rectangle. The remaining two side lengths would then need to add up to 46m - 1m - 22m = 23m. However, we can see that there are no other side lengths available to add up to 23m, so this combination does not work.
We will need to try other combinations until we have exhausted all possibilities:
1m, 2m, 3m, 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m, 15m, 16m, 17m, 18m, 19m, 20m, 21m, 22m, 23m, 24m, 25m
After going through all the combinations, we can count the number of rectangles that can be formed with a perimeter of 46m.
However, manually finding all the combinations could be time-consuming. Alternatively, we can use a formula to generate these combinations. The formula to calculate the number of rectangles with a given perimeter is:
Number of rectangles = (perimeter / 2) - 1
Using this formula, we can calculate the number of rectangles:
Number of rectangles = (46 / 2) - 1 = 22 - 1 = 21
Therefore, there are 21 different rectangles that can have a perimeter of 46m.