How many different rectangles can you make with aperimeter of 12 matchstick
Assuming that it is a square with three matchsticks on each side, matchsticks can be added internally to give nine squares with each side of one matchstick.
you need length+width=6, so
1x5
2x4
3x3
If you were angling for the more complex scenario proposed by PsyDAG, then things do get a bit trickier.
To find the number of different rectangles that can be made with a perimeter of 12 matchsticks, we need to consider the possible combinations of side lengths.
Let's assume the length is denoted by "l" and the width is denoted by "w". The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is given as 12 matchsticks. Therefore:
12 = 2 * (l + w)
Simplifying the equation, we have:
6 = l + w
Now, let's consider the possible combinations of lengths and widths that satisfy this equation. Keep in mind that the sides of a rectangle must be whole numbers greater than zero.
Here are the possible combinations:
1. l = 1, w = 5
In this case, the length is 1 matchstick and the width is 5 matchsticks.
2. l = 2, w = 4
Here, the length is 2 matchsticks and the width is 4 matchsticks.
3. l = 3, w = 3
In this case, both the length and the width are 3 matchsticks.
4. l = 4, w = 2
The length is 4 matchsticks and the width is 2 matchsticks.
5. l = 5, w = 1
Here, the length is 5 matchsticks and the width is 1 matchstick.
These are the five different rectangles that can be formed using 12 matchsticks.