"The area of a rectangle is 360m2. If its lengh if increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle." I need to use the "guess and test" or the "draw a diagram" method to solve; which would be most useful, and how would you go about solving the problem in general?
In this problem, you are asked to find the perimeter of the original rectangle given that the area remains the same even after changing its dimensions. Whether you choose to use the "guess and test" method or the "draw a diagram" method depends on your preference. However, I will explain both methods so you can choose the one that suits you best.
1. Guess and Test Method:
You can use the "guess and test" method by assuming different values for the length and width of the original rectangle until you find the correct dimensions that satisfy the given conditions.
Let's assume the original length of the rectangle is L and the original width is W. According to the problem, the area of the original rectangle is 360 m². Therefore, we have the equation:
L * W = 360
Now, you need to find the new length and width after the given changes. The problem states that the length is increased by 10m and the width is decreased by 6m, but the area doesn't change. So, we can form another equation:
(L + 10) * (W - 6) = 360
By solving these two equations simultaneously, you can determine the values of L and W. Once you have the length and width of the original rectangle, you can calculate the perimeter.
2. Draw a Diagram Method:
Alternatively, you can use the "draw a diagram" method to visualize the problem. Start by drawing a rectangle and labeling its length and width. Since the area of the original rectangle is 360 m², you can represent it on the diagram by shading the area.
Now, draw another rectangle adjacent to the original one, representing the modified dimensions. Since the modified rectangle has the same area, you can place equal signs between the shaded areas of the original and modified rectangles.
Next, represent the given changes on the diagram. If the length is increased by 10m, draw an arrow from the original rectangle's length with "+10" next to it. Similarly, if the width is decreased by 6m, draw an arrow from the original rectangle's width with "-6" next to it.
Using the diagram, you can see the relationship between the original and modified dimensions. By comparing different dimensions, you can determine the original length and width. Once you have these values, you can calculate the perimeter.
Both methods can lead you to the correct answer. Choose the one that you find most helpful based on your preferred problem-solving approach.