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Could a rectangle have a perimeter of 22 cm and an area of 20cm2?
Wiki User
∙ 14y ago
Let's try and find one and that will answer the question. We don't need to finish the job of finding one, just to get to the point where we can say yes or no for sure.
Let the length be L and the width be W
2L+2W=22
LW=20
So L=20/W
Now substitute that into the first equation
Yes
2(20/W)+2W=22
40/W+2W=22
(40+2W2 )/W=22
22W=(40+2W2 )
This is a quadratic equation
2W2 -22W+40=0
or
W2 -11W+20=0
We don't need to solve the equation to answer the question.
The discriminant ((-11)2 -4(20)=41 which is positive so there are two real roots. That means two values for W.
This tells us there is rectangle with those dimensions.
8.7 and 2.3 are the approximate dimensions of the desired rectangle, in case you want to know.
Wiki User
∙ 14y ago
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