Question 337072: Example of P > A
Example of P < A
Example of P = A
Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388)   (Show Source):
Answer by CharlesG2(834)  (Show Source):
You can put this solution on YOUR website! Example of P > A
Example of P < A
Example of P = A
if P is not perimeter, and A is not area then repost
A area = L length * W width
P perimeter = 2(L + W)
P > A --> 2(L + W) > LW --> 2L + 2W > LW
2L - LW > - 2W
LW - 2L < 2W (changed signs due to dividing by a negative)
L < 2W/(W - 2)
W = 4, L < 8/2 --> L < 4, but that would make the length the width and the width the length, so make it W < 4 and L = 4
example: L = 4 and W = 3
A = L * W = 4 * 3 = 12
P = 2(L + W) = 2(4 + 3) = 2 * 7 = 14
P > A
P < A --> 2(L + W) < LW --> 2L + 2W < LW
2L - LW < -2W
LW - 2L > 2W (changed signs due to dividing by a negative)
L > 2W/(W - 2)
W = 4, L > 8/2 --> L > 4
example: L = 5 and W = 4
A = L * W = 5 * 4 = 20
P = 2(L + W) = 2(5 + 4) = 2 * 9 = 18
P < A
if P = A then L * W = 2(L + W), and if L and W are whole numbers then L * W is an even number
L * W = 2(L + W) --> WL = 2L + 2W --> WL - 2L = 2W --> L = 2W/(W - 2)
if W = 0 --> L = 0/(-2) = 0 --> A = 0, P = 0, yes but zero by zero rectangle
if W = 1 --> L = 2/(-1) --> L = -2 --> that is not going to work
if W = 2 --> L = 4/0 --> that is not going to work
if W = 3 --> L = 6/1 --> L = 6, A = 3 * 6 = 18, P = 2(3 + 6) = 2 * 9 = 18
if W = 4 --> L = 8/2 --> L = 4, A = 4 * 4 = 16, P = 2(4 + 4) = 2 * 8 = 16,
this is a square, w = 0 and w = 4 are only squares for P = A
if W = 5 --> L = 10/3 = 3 1/3, A = 50/3, P = 50/3, length supposed to be longer than width so this is going in other direction
if W = 6 --> L = 3, A = 18, P = 18, this is same rectangle as W = 3, and this is last whole number combination
W > 2 if you want P = A
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