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anonymous
 5 years ago
A gardener has 120 feet of fencing to fence in a rectangular flower garden.
a) Find a function that models the area of the garden she can fence.
b) Can she fence a garden with an area of 850 square feet?
c) Find the dimensions of the largest area she can fence.
anonymous
 5 years ago
A gardener has 120 feet of fencing to fence in a rectangular flower garden. a) Find a function that models the area of the garden she can fence. b) Can she fence a garden with an area of 850 square feet? c) Find the dimensions of the largest area she can fence.

This Question is Closed

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0(a) P=2l+2w Perimeter=P=120 length=l width=w 120=2l+2w

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oops Area=A and since 120=2l+2w 60=l+w so w=60l so A=lw=l(60l)=60ll^2

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0there now a is complete

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, that makes sense.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0part b now) If A=850 then 850=60ll^2 l^260l+850=0 now we need to find l here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, so it's a quadratic equation...

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0right i don't think we can factor it but you use you use the quadratic formula

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok so if l=37.07 then w=6037.07 which is possible since the w is positive and if l=22.93, then is also possible since w is positive if we have this length

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So she can fence in a garden of 850 sq. feet?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0are you sure you got l=37.07 and 22.93

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{b \pm \sqrt{b^24ac}}{2a}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[l=(60\pm \sqrt{(60)^24(1)(850)}/2(1)\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{60 \pm \sqrt{60^24(1)(850)}}{2}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i got the lengths to be appoximately 52.93 and 67.07

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It would be \[60\pm14.14/2\]right?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0she can fence the garden as long as the length is less that 60 we have 52.93 so it is possible to fence an area of 850 square feet

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oops you are right lol

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok so remember from before w=60l?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we want w and l to be positive because negative lengths don't exist

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we want w to be positive so we want 60l>0 so 60>l (l<60)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0so do you think it is possible since both of the lengths we got are less than 60?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0does that make sense? 0<l<60

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, it does. Sorry I jsut ate dinner :P

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok find the vertex of A and you will find the maximum area put the A (which is a parabola) in vertex is form

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0A=60ll^2 A=l^2+60l A=(l^260l) A=(l^260l+(60/2)^2)+(60/2)^2 A=(l^260l+30^2)+30^2 A=(l30)^2+900 the vertex is (30,900) so max length is 30 and max area is 900
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