Question 814968
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.)