SOLUTION: The width of rectangle is 5ft less than the length. the area is 6ft^2, what is width and length?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The width of rectangle is 5ft less than the length. the area is 6ft^2, what is width and length?      Log On


   

Question 466723: The width of rectangle is 5ft less than the length. the area is 6ft^2, what is width and length?
Answer by gwendolyn(128) About Me  (Show Source):
You can put this solution on YOUR website!
We have two variables in this equation, width and length. We'll say that L=length and W=width.
The first piece of information we have is that the width is equal to the length minus 5 feet. This can be turned into an equation:
W=L-5
The other information we are provided is that the rectangle's area, which is equal to length times width, is 6 square feet. This too can be made into an equation:
L*W=6
We can plug the first equation into the second, since we have the variable 'W' isolated already.
L*(L-5)=6
Then, we can distribute the L.
L%5E2-5L=6
Subtract 6 from both sides.
L%5E2-5L-6=0
We can now factor this quadratic equation.
(L-6)(L+1)=0
This means that L is equal to either 6 or -1. Since L is a length, it has to be the positive option, so L=6.
We can now plug this value into the first equation to find the width.
6-5=W
1=W
Therefore, the width is 1 and the length is 6.