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) About Me  (Show Source):
You can put this solution on YOUR website!
AreaOfRectangle+=+Length+%2A+Width
Let Width be denoted by w
You are told Length+=+4+%2A+Width or Length=4w and the area = 196
So
AreaOfRectangle+=+Length+%2A+Width
196+=+%284w%29+%2A+w+
196+=+4w%5E2
46+=+w%5E2
So w = +- sqrt(46)
Sinvce the dimension cannot be negative, then w=sqrt(46)
Length = 4*w = 4*sqrt(46)

As a quadratic equation:
0+=+w%5E2+-+46
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-46+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-46=184.

Discriminant d=184 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+184+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+184+%29%29%2F2%5C1+=+6.78232998312527
x%5B2%5D+=+%28-%280%29-sqrt%28+184+%29%29%2F2%5C1+=+-6.78232998312527

Quadratic expression 1x%5E2%2B0x%2B-46 can be factored:
1x%5E2%2B0x%2B-46+=+1%28x-6.78232998312527%29%2A%28x--6.78232998312527%29
Again, the answer is: 6.78232998312527, -6.78232998312527. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-46+%29

Answer by MathTherapy(10552) About Me  (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: highlight_green%284w%5E2+-+196+=+0%29

4%28w%5E2+-+49%29+=+0

(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 = highlight_green%287%29 meters, and length = highlight_green%2828%29 meters.