Question

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?

Answer 1

P=18 and A = 18

P = 20 and A = 18

that what your asking for?

Answer 2

its possible, even easy...

Answer 3

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

Answer 4

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

Answer 5

Rectangle

Answer 6

i was hoping it was a rectangle :)

ok.... both areas need to be 18.

18 = lw right?

Answer 7

yeah

Answer 8

we can get a "value" for either l or w from this to use in the perimeter equations.

Lets say:

18/w = l good ?

Answer 9

yeah, thanks

Answer 10

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

Answer 11

yeah

Answer 12

so:

just use our "value" in this equation like this:

18 = 2(18/w) + 2w

Answer 13

ok

Answer 14

18 = 36/w + 2w.... lets get a common denominator to make life easy

18 = 36 + 2w^2
---------- still with me?
w

Answer 15

yeah, I'm with you

Answer 16

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

18w = 36 + 2w^2

Answer 17

yeah. I believe so

Answer 18

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?

Answer 19

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

Answer 20

ok

Yeah, we're ready =)

Answer 21

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?

Answer 22

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

Answer 23

ok

Answer 24

lets go for 20 :)

same steps but I aint gonna talk so much...

Answer 25

ok

Answer 26

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 :)

Answer 27

10 +- sqrt(100 -(4)(18))
---------------------
2

10 +- sqrt(28)
------------
2

w = 5 + sqrt(7) and l = 5-sqrt(7)

lets check them out

Answer 28

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

A = 25 - 7

A = 18

Answer 29

can i get you to help me with my problems

Answer 30

sure, just on sec please

Answer 31

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

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

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

P = 20

Answer 32

howd we do?

Answer 33

good, thanks!

Answer 34

lol... enjoy :)

Answer 35

:)

Answer 36

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