name the lengths of the sides of three rectangles that have perimeters of 14 units
P = 2L + 2W
14 = 2(5) + 2(2)
14 = 10 + 4
Can you think of other combinations?
4 and 3...5 and 2....6 and 1
To find the lengths of the sides of three rectangles with a perimeter of 14 units, we need to consider the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Let's denote the length of the rectangle as L and the width as W. We can then set up an equation for each rectangle using the given perimeter value:
1st rectangle: 14 = 2(L₁ + W₁)
2nd rectangle: 14 = 2(L₂ + W₂)
3rd rectangle: 14 = 2(L₃ + W₃)
To find the possible combinations of length and width that satisfy these equations, we can list the factors of 14 and explore their pairings:
Factors of 14: 1, 2, 7, 14
We can then list the possible combinations:
1st rectangle: (L₁, W₁) = (1, 6), (2, 5), (7, 0), (14, 0)
2nd rectangle: (L₂, W₂) = (1, 6), (2, 5), (7, 0), (14, 0)
3rd rectangle: (L₃, W₃) = (1, 6), (2, 5), (7, 0), (14, 0)
These are the potential lengths and widths for the three rectangles that have perimeters of 14 units. Note that in some cases (7, 0) and (14, 0), one side will have a length of 7 or 14 units, while the other side will have no length and is essentially a line segment.