SOLUTION: Write an equation that expresses side l as a function of the area A and the perimeter P. What must be the relationship between P and A if this equation has a real solution? So f

Algebra ->  Rectangles -> SOLUTION: Write an equation that expresses side l as a function of the area A and the perimeter P. What must be the relationship between P and A if this equation has a real solution? So f      Log On


   

Question 933128: Write an equation that expresses side l as a function of the area A and the perimeter P. What must be the relationship between P and A if this equation has a real solution?
So far, I've determined that A/w=l. I can replace w with ((P/2)-l). However, I don't know what to do from there.
Found 2 solutions by Alan3354, ewatrrr:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation that expresses side l as a function of the area A and the perimeter P. What must be the relationship between P and A if this equation has a real solution?
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If this is a rectangle:
Area = L*W --> W = A/L
P = 2L + 2W --> L = (P - 2W)/2
L = P/2 - A/L
L^2 = PL/2 - A
2L^2 - PL + A = 0
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L+=+P%2F4+%2B+sqrt%28P%5E2+-+4A%29%2F4

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
expresses s1 as a function of the area A and the perimeter P.
A%2Fs%5B2%5D+=+s%5B1%5D
.....
2s%5B1%5D+%2B+2s%5B2%5D+=+P+
s%5B1%5D+=+P%2F2+-s%5B2%5D
....
A%2Fs%5B2%5D+=+P%2F2+-+s%5B2%5D
A+=+%28P%2F2%29s%5B2%5D+-+%28s%5B2%5D%29%5E2
%28s%5B2%5D%29%5E2+-+%28P%2F2%29s%5B2%5D+%2B+A+=+0 format ax^2 + bx + c
...
Using DeterminantD+=++b%5E2-4%2Aa%2Ac+%29%29 Concept:
equation has a real solution IF:
(P/2)^2 - 4A ≥ 0