Math Is Fun Forum

draketcg

Member

Registered: 2012-08-03

Posts: 2

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!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

draketcg

Member

Registered: 2012-08-03

Posts: 2

Re: Need to find the smallest value for a rectangle with 40m² area.

Sweet. It's easy to understand if you explain this way, thanks a lot!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob