Max Area of Adjacent Rectangles: necessary assumptions?

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Keep your teacher "happy":
A = Area, L = Length, W = Width

2L + 3W = 480 [1]
A = LW [2]

[1]: 2L = 480 - 3W
L = (480 - 3W) / 2
Substitute in [2]:
A = W(480 - 3W) / 2
2A = W(480 - 3W)
continue...

Where in the problem statement - this relationship is indicated?

The problem does not say the rectangles are congruent!
 
The problem does not say the rectangles are congruent!

No, it does not. The problem does not provide any proportional information relating the two fields, either. So, I'm thinking that we need to assume congruency. If we don't make this assumption, could we calculate a numerical answer?

The problem also does not state that there is a fence line separating the two adjacent fields. I'm thinking that we need to assume there is. If we don't, could we calculate an answer that matches one of the multiple choices?
 
No, it does not. The problem does not provide any proportional information relating the two fields, either. So, I'm thinking that we need to assume congruency. If we don't make this assumption, could we calculate a numerical answer?

The problem also does not state that there is a fence line separating the two adjacent fields. I'm thinking that we need to assume there is. If we don't, could we calculate an answer that matches one of the multiple choices?
We do not need to postulate that both rectangles are congruent. What has been assumed is that the adjacent fields jointly form a rectangle. If that is not the case, I do not see that the problem is solvable. Of course, I somewhat doubt that SK was doing anything except busting the chops of monsieur denis, an admirable action to be applauded generally.
 
No, it does not. The problem does not provide any proportional information relating the two fields, either. So, I'm thinking that we need to assume congruency. If we don't make this assumption, could we calculate a numerical answer?

The problem also does not state that there is a fence line separating the two adjacent fields. I'm thinking that we need to assume there is. If we don't, could we calculate an answer that matches one of the multiple choices?

Agreed - but if we make assumptions beyond the problem statement - we should state those explicitly.
 
We do not need to postulate that both rectangles are congruent.

You're right; that's not needed. But it works, nonetheless.


What has been assumed is that the adjacent fields jointly form a rectangle.

This approach also works.


I somewhat doubt that SK was doing anything except busting the chops of monsieur denis …

OIC

I asked a moderator to move this off-topic discussion. ;)
 
We do not need to postulate that both rectangles are congruent. What has been assumed is that the adjacent fields jointly form a rectangle. If that is not the case, I do not see that the problem is solvable. Of course, I somewhat doubt that SK was doing anything except busting the chops of monsieur denis, an admirable action to be applauded generally.

So you mean in the original post - Denis had the last word!!!

Lookagain has been relatively silent recently - I thought it was my duty to make some trouble.....
 
Lookagain has been relatively silent recently - I thought it was my duty to make some trouble.....
Well the result is that Denis is now communicating from a different plane, where they say youze. He does not understand that in America the proper translation of vous is youns.
 
What would happen on the cricket ground, if each man tried to wear two hats simultaneously? :p

They do sometimes - not all 22 of them - but those players are called "all-rounders" (like Babe Ruth - can pitch and bat!!)
 
Why you guys picking on me :confused:
Choose one from:

(a) You have been slack in your corner duties.

(b) Your real name is Charlie Brown.

(c) The real Denis never visits the calculus room so you must an imposter.

(d) The OP cannot divide 240 by 3, and you expect derivatives.
 
it is about the maximum area of 2 rectangles and that is acheived with 2 congruent rectangles. Try to prove this by contradiction like a lot of mathematicians do.
 
it is about the maximum area of 2 rectangles and that is acheived (sic) with 2 congruent rectangles.

JeffM made a good point earlier, when he corrected my viewpoint that an assumption of congruent rectangles is needed.

We do not need to assume congruency. JeffM stated that it's sufficient to have two adjacent rectangular fields which together form a new rectangle.

In other words, the red fence line (below) separating the two fields may be slid to the left or to the right -- yielding two rectangular fields that are not congruent --without affecting the maximum area result.

playGround.jpg
 
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