Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2012-08-03 00:37:28

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?"

Offline

## #2 2012-08-03 01:09:57

bob bundy
Registered: 2010-06-20
Posts: 8,337

### 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

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

Offline

## #3 2012-08-03 01:21:31

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!

Offline

## #4 2012-08-03 01:26:48

bob bundy
Registered: 2010-06-20
Posts: 8,337

### 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

Offline