SOLUTION: I need help with this one , i am struggling in this calss and it is about to end and I need to get help badly... We appreciate your help and God bless ya. Here"s the question: Tra

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Question 203985: I need help with this one , i am struggling in this calss and it is about to end and I need to get help badly... We appreciate your help and God bless ya. Here"s the question: Translate the following into a quadratic equation and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 quare meters, what are it's dimensions?
Found 2 solutions by vleith, MathTherapy:
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!

Let Width be denoted by w
You are told or and the area = 196
So




So w = +- sqrt(46)
Sinvce the dimension cannot be negative, then w=sqrt(46)
Length = 4*w = 4*sqrt(46)

As a quadratic equation:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=184 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.78232998312527, -6.78232998312527. Here's your graph:
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Let width of garden be w
Since length is 4 times width, then length = 4w
Since the area of the garden is 196 square meters, then we'll have: w(4w) = 196

QUADRATIC EQUATION:



(w - 7)(w + 7) = 0

w = 7 , or - 7

The negative value (-7) is rejected because you CANNOT have a negative measurement for width.

Therefore, w, or width of garden = meters, and length = meters.





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