Is it possible to change a figure with an area of 18 and a perimeter of 18 to a perimeter of 20, but with the same area?

- anonymous

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- amistre64

P=18 and A = 18
P = 20 and A = 18
that what your asking for?

- amistre64

its possible, even easy...

- anonymous

I need to change the perimeter, but leave the area the same

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- amistre64

what shape are you needing to change? rectangle, triangle, pentaangle?

- anonymous

Rectangle

- amistre64

i was hoping it was a rectangle :)
ok.... both areas need to be 18.
18 = lw right?

- anonymous

yeah

- amistre64

we can get a "value" for either l or w from this to use in the perimeter equations.
Lets say:
18/w = l good ?

- anonymous

yeah, thanks

- amistre64

p = 2l + 2w 4 sides all together, 2 of each right?

- anonymous

yeah

- amistre64

so:
just use our "value" in this equation like this:
18 = 2(18/w) + 2w

- anonymous

ok

- amistre64

18 = 36/w + 2w.... lets get a common denominator to make life easy
18 = 36 + 2w^2
---------- still with me?
w

- anonymous

yeah, I'm with you

- amistre64

tell me when I do something stupid :) we can multiply that bottom "w" across to the 18 right?
18w = 36 + 2w^2

- anonymous

yeah. I believe so

- amistre64

we can...
now put all like terms to one side
0 = 2w^2 -18w +36
we are ready to find out what w can be right?

- amistre64

all terms to one side is what I meant to type :)

- anonymous

ok
Yeah, we're ready =)

- amistre64

factor out the 2, its in our way
0 = 2(w^2 -9w +18)
now we know that anything times zero = zero, our only choice is to make that left part equal to zero.
w^2 -9w +18 = 0
(w-6) (w-3) = 0
when w = 6 or 3 are good. actually w can stand for length or width here so we found both numbers :)
lets try it our:
A = 6(3) = 18
P = 2(6) + 2(3)
P = 12 + 6 = 18 were good for that one right?

- amistre64

and by left I mean right..... its like haveing a stroke....

- anonymous

ok

- amistre64

lets go for 20 :)
same steps but I aint gonna talk so much...

- anonymous

ok

- amistre64

20 = 2(18/w) + 2w
20 = 36/w + 2w
20 = 36 + 2w^2
----------
w
20w = 36 +2w^2
0 = 2w^2 -20w +36
0 = 2(w^2 -10w +18)
w^2 -10w +18 = 0
now this one we use the quadratic formula on because it wont behave for us :)

- amistre64

10 +- sqrt(100 -(4)(18))
---------------------
2
10 +- sqrt(28)
------------
2
w = 5 + sqrt(7) and l = 5-sqrt(7)
lets check them out

- amistre64

A = (5-sqrt(7)) (5+sqrt(7))
A = 25 - 7
A = 18

- anonymous

can i get you to help me with my problems

- amistre64

sure, just on sec please

- amistre64

P = 2(5-sqrt(7)) + 2(5+sqrt(7))
P = 10 -2sqrt(7) + 10 + 2sqrt(7)
P = 20 +2sqrt(7) -2sqrt(7)
P = 20

- amistre64

howd we do?

- anonymous

good, thanks!

- amistre64

lol... enjoy :)

- anonymous

:)

- anonymous

i have to go now. Bye, and thanks again!

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