Hi,

 a = (((L*W = 4CM^2}}}  L = 4/W



Question states*** perimeter is 10 cm. 

 

     

      

      

       (W-4)=0 , W = 1cm , L = 4cm

      (W-1) = 0, W = 4cm , L = 1cm

Dimension are 4cm by 1cm

CHECKING our answer***

        

 

Answer by FightinBlueHens(27)   (Show Source): You can put this solution on YOUR website!
 1. First let's start with the information that you know. 

2. We need to represent this information to solve it.

3. We will represent this information in 2 equations. Start with what you know.

4. We know we are dealing with a rectangle, and the area of a rectangle can be represented by width x height. We're going to call the width the base

5. Let the base=x, and the height=y so the formula for the area is x*y=4.

6. We know that the perimeter of a rectangle is equal to the the length of all 4 sides, so two times the height plus 2 times the base. This can be represented by 2x+2y= 10 (because we know that the perimeter equals 10).



First you need to solve for one variable, so let's start with the problem 2x+2y=10.



2x+2y=10.



2y=10-2x  (Here you move the term 2x to the opposite side by subtracting it from one side, and then doing the same thing to the other side.)



2y/2=(10/2)-(2x/2) You want just the variable (y) on one side so divide both sides by 2.



y=5-x  Now you know what y equals, so you can plug this variable in to the first equation.



x*y=4 --> x*(5-x)=4



5x-x^2=4 Distribute.



-x^2+5x-4=0 Bring all the terms to one side so you can solve for x, and write the equation in standard form so that you can solve it more easily.



(-x+1)(x-4)=0 Factor the equation 



Here there are two possible answers.



[(-x+1)(x-4)]/(x-4)=0/(x-4) Divide both sides by x-4 to figure out one of the answers.



-x+1=0  This is the answer to dividing both sides by x-4



-x=-1 Subtract 1 from both sides.



x=1 Multiply both sides by negative one to find out the positive value of x. This is a positive number, that can be one answer to your problem.



Do the other side



[(-x+1)(x-4)]/(-x+1)= 0/(-x+1) Divide (-x+1)(x-4)=0 by (-x+1) on both sides to solve for (x-4)



x-4=0



x=4



Your answers are x=1 and x=4.  Now plug these answers back into the original equation xy=4.



4y=4



y=1 Divide both sides by 4.



1y=4



y=4 (Divide both sides by 1)



1 and 4 can be in the place of x or y because they give you the same answer.



As for the perimeter 2x+2y=10:



2*4+2*1= 8+2



8+2=10 (This's the perimeter.)











 

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