anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
P=18 and A = 18 P = 20 and A = 18 that what your asking for?
amistre64
  • amistre64
its possible, even easy...
anonymous
  • anonymous
I need to change the perimeter, but leave the area the same

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amistre64
  • amistre64
what shape are you needing to change? rectangle, triangle, pentaangle?
anonymous
  • anonymous
Rectangle
amistre64
  • amistre64
i was hoping it was a rectangle :) ok.... both areas need to be 18. 18 = lw right?
anonymous
  • anonymous
yeah
amistre64
  • 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
  • anonymous
yeah, thanks
amistre64
  • amistre64
p = 2l + 2w 4 sides all together, 2 of each right?
anonymous
  • anonymous
yeah
amistre64
  • amistre64
so: just use our "value" in this equation like this: 18 = 2(18/w) + 2w
anonymous
  • anonymous
ok
amistre64
  • amistre64
18 = 36/w + 2w.... lets get a common denominator to make life easy 18 = 36 + 2w^2 ---------- still with me? w
anonymous
  • anonymous
yeah, I'm with you
amistre64
  • amistre64
tell me when I do something stupid :) we can multiply that bottom "w" across to the 18 right? 18w = 36 + 2w^2
anonymous
  • anonymous
yeah. I believe so
amistre64
  • 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
  • amistre64
all terms to one side is what I meant to type :)
anonymous
  • anonymous
ok Yeah, we're ready =)
amistre64
  • 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
  • amistre64
and by left I mean right..... its like haveing a stroke....
anonymous
  • anonymous
ok
amistre64
  • amistre64
lets go for 20 :) same steps but I aint gonna talk so much...
anonymous
  • anonymous
ok
amistre64
  • 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
  • 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
  • amistre64
A = (5-sqrt(7)) (5+sqrt(7)) A = 25 - 7 A = 18
anonymous
  • anonymous
can i get you to help me with my problems
amistre64
  • amistre64
sure, just on sec please
amistre64
  • 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
  • amistre64
howd we do?
anonymous
  • anonymous
good, thanks!
amistre64
  • amistre64
lol... enjoy :)
anonymous
  • anonymous
:)
anonymous
  • anonymous
i have to go now. Bye, and thanks again!

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