How many shapes have a perimiter that's 30 cm?
Any shape can have a perimeter of 30 cm, both regular and irregular.
see http://en.wikipedia.org/wiki/Polygon
all but a circle
2x_+2 x width = perimeter
To find out how many shapes have a perimeter of 30 cm, we need to consider different shapes and their respective perimeters.
Let's start with a rectangle:
A rectangle has two pairs of equal sides. So, assuming the sides are x and y, its perimeter is given by the formula: 2x + 2y = 30 cm.
This can be simplified to x + y = 15 cm.
Now, we can list the possible combinations of values for x and y that satisfy this equation:
- x = 1 cm, y = 14 cm
- x = 2 cm, y = 13 cm
- x = 3 cm, y = 12 cm
- x = 4 cm, y = 11 cm
- x = 5 cm, y = 10 cm
- x = 6 cm, y = 9 cm
- x = 7 cm, y = 8 cm
- x = 8 cm, y = 7 cm
- x = 9 cm, y = 6 cm
- x = 10 cm, y = 5 cm
- x = 11 cm, y = 4 cm
- x = 12 cm, y = 3 cm
- x = 13 cm, y = 2 cm
- x = 14 cm, y = 1 cm
So, there are 14 possible rectangles with a perimeter of 30 cm.
Next, let's consider a square:
In a square, all sides are equal.
Therefore, if each side is x, the perimeter of a square is given by the formula: 4x = 30 cm.
Simplifying this equation, we find x = 7.5 cm.
However, since the question asks for the perimeter to be an integer value, we can't have a square with sides measuring 7.5 cm. This means there are no squares with a perimeter of 30 cm.
Finally, let's consider a triangle:
In a triangle, the sum of any two sides must be greater than the third side for it to be a valid shape.
So, let's try different combinations that satisfy this condition:
- x = 10 cm, y = 10 cm, z = 10 cm (equilateral triangle): perimeter is 30 cm.
- x = 5 cm, y = 15 cm, z = 10 cm (isosceles triangle): perimeter is 30 cm.
- x = 12 cm, y = 8 cm, z = 10 cm (scalene triangle): perimeter is 30 cm.
So, there are three possible triangles with a perimeter of 30 cm.
In conclusion, there are 14 rectangles, no squares, and three triangles that have a perimeter of 30 cm.