Question 159212
The area of a rectangle is Length*Width
In this example X=width Y=Length

We know that the area of the rectangle is- XY=38
We know that the length of the fence that surrounds 3 sides =18
The algebraic equation for this is X+Y+X=18=2X+Y=18

We alter the perimeter equation to isolate the Y variable
2X+Y=18
Subtract 2X from both sides
Y=18-2X

Substitute 18-2X for Y in the area equation.


X(18-2X)=38

18X-2x^2=38

Rearrange terms to reflect a quadratic equation

-2x^2+18x-38=0



*[invoke solve_quadratic_equation -2, 18, -38]

There are two solutions to this problems X=5.6180 and X=3.381

If we use X value of 5.6180 we can plug to find out Y value Y=18-2X 

Y is 6.764    (5.6180)(6.764)=38.000152

Length of the patio is 6.764 meters and the width of the patio is 5.6180 meters