Question 1150246: The perimeter of a parallelogram is 22cm and its area is 24 square cm.
What are the lengths of its sides?
This was a question posed to my son for his grade 7 math homework. This is supposed to be for a single parallelogram, not two. After struggling with this, I determined this is not possible to have these measurements for the same singular shape.
The dimensions could work out if the short side is 3cm and the long side is 8cm, for two separate parallelograms, but not one singular parallelogram.
Please tell me if I am right or wrong.
Thanks.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The perimeter of a parallelogram is 22cm and its area is 24 square cm.
What are the lengths of its sides?
This was a question posed to my son for his grade 7 math homework. This is supposed to be for a single parallelogram, not two. After struggling with this, I determined this is not possible to have these measurements for the same singular shape.
The dimensions could work out if the short side is 3cm and the long side is 8cm, for two separate parallelograms, but not one singular parallelogram.
Please tell me if I am right or wrong.
Thanks.
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It's a rectangle, which is still a parallelogram.
The sides are 3 and 8.
Perimeter = 2W + 2L = 22
Area = 3*8 = 24
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The rectangle is the only solution.
The p'gram with the minimum perimeter for a given are is a rectangle.
No other parallelograms fit.
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You have 2 different answers.
Post the problem again with my comments, unless Ikleyn responds.
She's wrong about this one.
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
From the given conditions, the sides of a parallelogram CAN NOT be determined by an unique way.
There are INFINITELY MANY possible solutions/answers.
If the shape is a RECTANGLE, then the unique answer is possible: 8 cm and 3 cm.
For parallelogram, there is no a unique answer. There are infinitely many possible configurations.
As the problem was given, it is a F A K E problem.
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