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(a) P=2l+2w
Perimeter=P=120
length=l
width=w
120=2l+2w

oops Area=A
and since 120=2l+2w
60=l+w
so w=60-l
so A=lw=l(60-l)=60l-l^2

there now a is complete

Okay, that makes sense.

part b now) If A=850
then
850=60l-l^2
l^2-60l+850=0
now we need to find l here

Oh, so it's a quadratic equation...

right i don't think we can factor it but you use you use the quadratic formula

what did you get?

l=37.07 or l=22.93

So she can fence in a garden of 850 sq. feet?

are you sure you got l=37.07 and 22.93

Yeah...

a=1
b=-60
c=850
?

\[\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

\[l=(60\pm \sqrt{(-60)^2-4(1)(850)}/2(1)\]

\[\frac{60 \pm \sqrt{60^2-4(1)(850)}}{2}\]

Yeah.

i got the lengths to be appoximately 52.93 and 67.07

It would be \[60\pm14.14/2\]right?

let me try again

oops you are right lol

ok so remember from before w=60-l?

we want w and l to be positive because negative lengths don't exist

we want w to be positive so we want 60-l>0
so 60>l (l<60)

so do you think it is possible since both of the lengths we got are less than 60?

and greater that 0?

than*

does that make sense?
0

Yeah, it does. Sorry I jsut ate dinner :P

Ohhhh okay :D