Question

What is the largest possible area for a rectangle with a perimeter of 80 cm?

Answer 1

How do I do this?

Answer 2

assumed that rectangle be a square
what is the area of a square which has perimeter = 80 ?

Answer 3

you have to determine its side of the square

Answer 4

@RadEn it would be 20 each side if it was a square

Answer 5

Imagine one side is X. The other side will be Perimeter/2-X=40-X
Area will be: \[A=X·(40-X)=40X-X^2\]Find the maximum for the function A:
\[dA/dX=0 \rightarrow 40-2X=0 \rightarrow X=20\]So one side is X=20 and the other 40-X=20. It is a square with side 20---->Max Area=400

Answer 6

yes,
so the area = side * side = 20 * 20 = 400

Answer 7

yes it would be 400 @RadEn

Answer 8

wait?! @RadEn @CarlosGP okay so I have ....

Answer 9

okay, is it like this

Answer 10

?????

Answer 11

No, it is x and 40-x

Answer 12

oh ya huh haha okay sorry about that. let me try again

Answer 13

? like this?

Answer 14

@CarlosGP

Answer 15

Yes, so the area is A=x·(40-x) right?

Answer 16

yes it is. haha sorry i was looking at it again

Answer 17

You cannot say it is a square, you need to prove it has to be a square. Then find the maximum of the polynomial function A=x(40-x) and you will get that happens when x=20

Answer 18

okay, cuz if it was a square it would be easier. but in this case the answer would be as you say A=x(40-x) right? because half of 80 is 40, and we have to subtract x from that 40 because we do not know what x is exactly. @CarlosGP

Answer 19

@CarlosGP

Answer 20

That is right.

Answer 21

YAY!!! THANK YOU!! :D okay, i have one more question im going to post.

Answer 22

u r welcome!
Please, close this one and create a new post

Answer 23

I already did :)

Answer 24

the rectangle would has the largest area if its length = width
that's the property of a square, no prove here because obviouly would has same answer if you do by using calculus :) @CarlosGP

Answer 25

More useful to learn calculus than learning by heart the properties of a rectangle

Answer 26

depent what level the student is studying it. if just for basic, i think calculus not yet ready get it .
note :
"if the length of rectangle not same with the width, the area cant be maximum."
for @lilsis76