Problems Involving Quadratic Equations

[Florence Chua]

Hi! I am a high school student and I cannot find examples of the problem I find difficult to solve. I already searched in many sites and I also watched in YouTube but there are no examples at all. This is the problem:

Produce a picture frame that has an area of 64 sq. meters; the combination of the frame itself and the space where the picture is shown. Provide the length and width of it as well as the explanation.

My problem now is how do I solve the length and width of the picture frame when the area is the only given. The examples that I found in the internet are just problems in solving the missing values of the length and width of the frame.

Thank you in advance for the help! It's really a great help.

 

[Deleted member 4993]

Hi! I am a high school student and I cannot find examples of the problem I find difficult to solve. I already searched in many sites and I also watched in YouTube but there are no examples at all. This is the problem:

Produce a picture frame that has an area of 64 sq. meters; the combination of the frame itself and the space where the picture is shown. Provide the length and width of it as well as the explanation.

My problem now is how do I solve the length and width of the picture frame when the area is the only given. The examples that I found in the internet are just problems in solving the missing values of the length and width of the frame.

Thank you in advance for the help! It's really a great help.

If you have posted the problem COMPLETELY and CORRECTLY, then it cannot be solved.

If you post a picture of the original problem, may be we can assist you to find additional parameters to solve the problem.

 

[Dr.Peterson]

Hi! I am a high school student and I cannot find examples of the problem I find difficult to solve. I already searched in many sites and I also watched in YouTube but there are no examples at all. This is the problem:

Produce a picture frame that has an area of 64 sq. meters; the combination of the frame itself and the space where the picture is shown. Provide the length and width of it as well as the explanation.

My problem now is how do I solve the length and width of the picture frame when the area is the only given. The examples that I found in the internet are just problems in solving the missing values of the length and width of the frame.

Thank you in advance for the help! It's really a great help.

There is no one correct solution if you know only the area and nothing else. it could be 1 by 64 meters, or 8 by 8 meters, or 2 by 32 meters, or whatever. (But how big a wall is this picture to be hung on??)

As stated, "produce A picture frame", any of these, or infinitely many more, would be a valid answer. The hard part would be to actually make the frame! They aren't asking for a single unique answer, but are looking for the explanation.

Why do you think this involves a quadratic equation?

 

[Florence Chua]

There is no one correct solution if you know only the area and nothing else. it could be 1 by 64 meters, or 8 by 8 meters, or 2 by 32 meters, or whatever. (But how big a wall is this picture to be hung on??)

As stated, "produce A picture frame", any of these, or infinitely many more, would be a valid answer. The hard part would be to actually make the frame! They aren't asking for a single unique answer, but are looking for the explanation.

Why do you think this involves a quadratic equation?

Thank for your time in answering my question! Our discussion was all about quadratic equations, and my teacher told us to produce a picture frame with an area of 64 sq. meters. Plus, he told us to explain our work and solve the given problem despite the area was the only thing provided. He said that in order for us to solve the problem we need to apply our lessons in quadratic equations.

 

[Dr.Peterson]

My guess would be that this is intended simply to get you to think about the underlying ideas, perhaps those about area, or even about what it means to solve a problem (that there may not be a unique solution). Likely this can involve looking through example problems you have, and seeing how they are different from this one.

On the other hand, you could add a constraint of your own, such as that the perimeter is 40 meters, or that the length and width are in the ratio 2:1, and find a solution in that case (likely using a quadratic equation). There are many ways you can explore the question.

 

[Florence Chua]

Thank you so much! It's really a great help. I think, I kind of understand the problem now because of your answer. I will try to look more unto it.

My guess would be that this is intended simply to get you to think about the underlying ideas, perhaps those about area, or even about what it means to solve a problem (that there may not be a unique solution). Likely this can involve looking through example problems you have, and seeing how they are different from this one.

On the other hand, you could add a constraint of your own, such as that the perimeter is 40 meters, or that the length and width are in the ratio 2:1, and find a solution in that case (likely using a quadratic equation). There are many ways you can explore the question.

Thank you so much! I kind of understand the problem now because of your answer. I will look more into it and ask my teacher for clarifications as well. Perhaps what you said was his objective in the first place.