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#1 2012-08-03 22:37:28
- draketcg
- Novice
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Need to find the smallest value for a rectangle with 40m² area.
Hi.
It's basically this, I got some questions in this style and I can't find a way to solve it. This is one of them:
"Paul has enough materials to build up a 24m fence. He wants to surround a 40m² rectangular terrain. Is that possible? If not, what's the maximum rectangular area Paul can reach with those materials?"
Please show your work.
Thanks in advance!
#2 2012-08-03 23:09:57
- bob bundy
- Moderator
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Re: Need to find the smallest value for a rectangle with 40m² area.
hi draketcg
Welcome to the forum!
If you call the length x then the width must be (24 - 2x)/2 = 12 - x
So the area is x(12-x)
So the question is, can you make that equal to 40 ?
If you try to solve that using the quadratic formula:
There are no real values of x to solve that square root so it would seem it is not possible.
To find the biggest area I'll make a graph first :
You can see from the graph ( at the end ) that the maximum is below 40, so that confirms the statement above.
Quadratics are symmetrical so the maximum will be at x = 6
Or use calculus to find the maximum.
So biggest area = 6(12-6) = 36
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#4 2012-08-03 23:26:48
- bob bundy
- Moderator
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Re: Need to find the smallest value for a rectangle with 40m² area.
You're welcome.
If you have more like this, see how far you can get on your own, and post again if you get stuck.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
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