If x is the length and y is the width of a rectangle, find and graph all integer pairs(x,y) that create a rectangle with a perimeter of 12 cm.
(1,5)
(2,4)
(3,3)
(4,2)
(5,1)
To find and graph all integer pairs of (x, y) that create a rectangle with a perimeter of 12 cm, we can use the perimeter formula for a rectangle:
Perimeter = 2 * (Length + Width)
Given that the perimeter is 12 cm, we can set up the equation:
12 = 2 * (x + y)
Dividing both sides of the equation by 2, we get:
6 = x + y
Now, we can find all the possible integer pairs (x, y) that satisfy this equation.
First, let's consider the possible values for x. Since the length of a rectangle cannot be negative or zero, x must be a positive integer. We can use trial and error to determine all the possible integer values for x:
If x = 1, then y = 6 - x = 6 - 1 = 5
If x = 2, then y = 6 - x = 6 - 2 = 4
If x = 3, then y = 6 - x = 6 - 3 = 3
If x = 4, then y = 6 - x = 6 - 4 = 2
So, the possible integer pairs (x, y) that create a rectangle with a perimeter of 12 cm are:
(1, 5), (2, 4), (3, 3), (4, 2)
Now, let's graph these integer pairs on a coordinate plane. Put the values of x on the x-axis and the values of y on the y-axis.
The graph will have four points: (1, 5), (2, 4), (3, 3), (4, 2). Connect these points with lines, and you will have a visual representation of all the rectangles that satisfy the given conditions.
Please note that the question asks for integer pairs (x, y), so we consider only whole numbers.