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Year 12s: what will be the first way you research your future options? >>

Calculus

Hi all,

How would I go about answering question 7 part ii?

Thanks

IMG_6375.jpg465.2KB

If you have a rectangle with side lengths

x

and

y

say, then the perimeter,

P

is given as

2(x+y)

, and the area is 100 but the area is also given by

xy

so

xy=100

. Can you think of where to go from there?

You can pose a rectangle of dimensions

x

and

y

, whose area is

x \cdot y = 100 m^2

.
It's perimeter is equal to

2 \cdot (x+y)

.
Hint:

Spoiler

(edited 7 years ago)

OP

The only thing I can think of is to differentiate the area and then put it into the perimeter equation ??

OP

Original post by MartyO

You can pose a rectangle of dimensions

x

and

y

, whose area is

x \cdot y = 100 m^2

.
It's perimeter is equal to

2 \cdot (x+y)

.
Hint:

Spoiler

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 :frown:

:frown:

(edited 7 years ago)

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.

OP

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 ?

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.

OP

Original post by B_9710

All rectangles are squares, just like all rectangles are parallelograms.

Ahh right (you learn something new everyday :smile:

:smile:

) thanks haha

so would the dimensions be 10 by 10 then ?

Original post by Olive123

Ahh right (you learn something new everyday :smile:

:smile:

) thanks haha

so would the dimensions be 10 by 10 then ?

Yes.

OP

Original post by B_9710

Yes.

Thank you sooooooo much :biggrin:

:biggrin:

:biggrin:

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! :smile:

:smile:

Original post by Olive123

Ahh right (you learn something new everyday :smile:

:smile:

) 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.

Original post by davros

I think you mean "all squares are rectangles" - I can think of plenty of rectangles that aren't squares! :smile:

:smile:

Of course mate, got my words mixed up.

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