Describe a real world relationship between the area of a rectangle and its width, as the width varies and the length at the same time. Sketch a graph to show the relationship.
So far, I have that even when the width increases, the width times the length always equals the area. Am I missing anything? How do I sketch a graph?
assertion is true, but it's tough to sketch, since the area is a function of two variables, requiring a 3-D graph.
How can I sketch this? I have to do it on paper.
only way is to have a fixed value for one of the variables.
For instance, if the area remains constant, then if the sides are x and y, you have (if the area is, say, 20)
xy = 20
y = 20/x
Now plot a few points and you will see how the curve looks.
You are correct that the area of a rectangle is determined by multiplying its width and length together. As one variable changes while the other remains constant, it affects the value of the area. Let's go step by step and describe the relationship between the area and width of a rectangle while keeping the length constant:
1. If you hold the length constant, when the width increases, the area of the rectangle also increases. This is because increasing the width expands the base of the rectangle, which in turn increases the overall area.
2. On the other hand, if you decrease the width, the area decreases as well. Decreasing the width reduces the base of the rectangle, thus leading to a smaller overall area.
To sketch a graph showing the relationship between the area and width of a rectangle, you can utilize a coordinate plane. The x-axis represents the width, while the y-axis represents the area. Here's how you can proceed with drawing the graph:
1. Assign suitable numerical values or intervals to the x-axis (width), depending on the range you want to represent.
2. Use the equation A = w * L to calculate the area corresponding to various width values, assuming a fixed length L. For instance, if the length is 5 units, you can calculate the corresponding area (A) for various width (w) values:
- If w = 2, A = 2 * 5 = 10
- If w = 4, A = 4 * 5 = 20
- If w = 6, A = 6 * 5 = 30
- ...
3. Plot the width (w) on the x-axis and the calculated area (A) on the y-axis.
4. Connect the plotted points with a line to demonstrate the relationship between the width and the area. This line should rise as w increases, indicating that the area increases with the width.
Remember, this graph is specific to a given length (L), and changing the length value would result in a different graph.