SOLUTION: If rectangle ABCD has a larger area than rectangle EFGH, does it follow that ABCD must have a perimeter larger than that of EFGH? Argue why or why not

Algebra ->  Triangles -> SOLUTION: If rectangle ABCD has a larger area than rectangle EFGH, does it follow that ABCD must have a perimeter larger than that of EFGH? Argue why or why not      Log On


   

Question 312989: If rectangle ABCD has a larger area than rectangle
EFGH, does it follow that ABCD must have a
perimeter larger than that of EFGH? Argue why or
why not
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
a 4 by 5 rectangle has an area of 20 and a perimeter of 18

a 1 by 15 rectangle has an area of 15 and a perimeter of 32

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Absolutely not. Consider a rectangle that is 500 meters long and millimeter wide. This rectangle has a perimeter slightly larger than 1000 meters but an area that is only 0.05 square meters. Then consider a rectangle that is 1 meter by 1 meter which only has a perimeter of 4 meters (250 times smaller than the first rectangle) but an area of 1 square meter (20 times greater than the first rectangle)


John