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# Calculus

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1. Hi all,

Thanks
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2. If you have a rectangle with side lengths and say, then the perimeter, is given as , and the area is 100 but the area is also given by so . Can you think of where to go from there?
3. You can pose a rectangle of dimensions and , whose area is .
It's perimeter is equal to .
Hint:
Spoiler:
Show
Using those formulas, you have to define the perimeter with respect to one side, with the constraint of the area.
You then derive that expression of the perimeter, and find the turning point. Given the context, it will be a local minimum.
4. The only thing I can think of is to differentiate the area and then put it into the perimeter equation ??
5. (Original post by MartyO)
You can pose a rectangle of dimensions and , whose area is .
It's perimeter is equal to .
Hint:
Spoiler:
Show
Using those formulas, you have to define the perimeter with respect to one side, with the constraint of the area.
You then derive that expression of the perimeter, and find the turning point. Given the context, it will be a local minimum.
Is x equal to +/- 10?

Ok so I did y=100/x from the area equation. Then I subbed it into the perimeter equation and differentiated and solved for x by putting it equal to zero. I got x=+/- 10 . However, if i sub that x into the area equation I get y also equals 10 which doesnt make sense if its a rectangle
6. (Original post by Olive123)
Is x equal to +/- 10?
x>0 since it represents length. So the rectangle is in fact a square. In fact for any rectangle,the rectangle will have greatest perimeter for any given area if and only if it is a square.
7. (Original post by B_9710)
x>0 since it represents length. So the rectangle is in fact a square. In fact for any rectangle,the rectangle will have greatest perimeter for any given area if and only if it is a square.
So is my answer wrong ?

How can a rectangle be a square ?
8. (Original post by Olive123)
So is my answer wrong ?

How can a rectangle be a square ?
All rectangles are squares, just like all rectangles are parallelograms.
9. (Original post by B_9710)
All rectangles are squares, just like all rectangles are parallelograms.
Ahh right (you learn something new everyday ) thanks haha

so would the dimensions be 10 by 10 then ?
10. (Original post by Olive123)
Ahh right (you learn something new everyday ) thanks haha

so would the dimensions be 10 by 10 then ?
Yes.
11. (Original post by B_9710)
Yes.
Thank you sooooooo much
12. (Original post by B_9710)
All rectangles are squares, just like all rectangles are parallelograms.
I think you mean "all squares are rectangles" - I can think of plenty of rectangles that aren't squares!

(Original post by Olive123)
Ahh right (you learn something new everyday ) thanks haha

so would the dimensions be 10 by 10 then ?
As above, a square is just a special case of a rectangle in which all the sides are equal.
13. (Original post by davros)
I think you mean "all squares are rectangles" - I can think of plenty of rectangles that aren't squares!
Of course mate, got my words mixed up.

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