- #1
mercedesbenz
- 15
- 0
Homework Statement
please help me find maximum area of ABCD
In summary, the conversation is about finding the maximum area of a polygon with four points, ABCD. The suggestion is to come up with a function representing the area and then find its maximum by using its derivative and critical points. The person asking for help is advised to show their work and to start by fixing three points and finding the best position for the fourth point.
please help me find maximum area of ABCD
- #2
sutupidmath
- 1,630
- 4
Well it looks like you have enough information there to come up with a function that represents the area of that polygon. After that see where that function has a maximum. That is take its derivative and find critical points, and plug them into your original function, and see what values you get.
You need to show some work of yours, if you want to get more help!
Cheers!
You need to show some work of yours, if you want to get more help!
Cheers!
- #3
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
… a bit at a time ! …
Hi mercedesbenz!
This is one of those problems that is a bit complicated to do all in one go.
So simplify it … do a bit at a time!
Hint: fix A B and D, and just find the best place for C.
Solve that, and the rest of the problem becomes obvious.
Hi mercedesbenz!
This is one of those problems that is a bit complicated to do all in one go.
So simplify it … do a bit at a time!
Hint: fix A B and D, and just find the best place for C.
Solve that, and the rest of the problem becomes obvious.
1. How do you determine the maximum area of ABCD?
The maximum area of ABCD can be determined by using the formula A = bh, where b represents the base and h represents the height of the rectangle. In order to find the maximum area, the base and height must be optimized to create the largest possible rectangle.
2. What are the steps to find the maximum area of ABCD?
The steps to find the maximum area of ABCD are as follows:
1. Identify the length and width of the rectangle.
2. Use the formula A = bh to find the area of the rectangle.
3. Modify the length and width to find the combination that produces the largest area.
4. Once the maximum area is found, use the optimized length and width to create the rectangle ABCD with the largest possible area.
3. Can the maximum area of ABCD be found without using a formula?
Yes, the maximum area of ABCD can be found using geometric reasoning. By understanding the properties of rectangles, one can determine that the maximum area occurs when the rectangle is a square, as all sides are equal. Therefore, the maximum area of ABCD can be found by finding the length and width of the square with the same perimeter as ABCD.
4. Is there a specific method or algorithm to find the maximum area of ABCD?
Yes, there are multiple methods and algorithms that can be used to find the maximum area of ABCD. Some commonly used methods include using derivatives to find the maximum value of a function, using trial and error to test different combinations of length and width, and using geometric reasoning as mentioned in the previous answer.
5. Can the maximum area of ABCD be found if the dimensions of the rectangle are not given?
No, the maximum area of ABCD cannot be found if the dimensions of the rectangle are not given. The length and width are necessary in order to calculate the area and optimize it for the maximum value. Without this information, the maximum area cannot be determined.
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