SOLUTION: The length of a rectangle is 2feet less than 3times its width . Find the length and width if the area of the garden is 21 square feet

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Question 46952: The length of a rectangle is 2feet less than 3times its width . Find the length and width if the area of the garden is 21 square feet
Answer by aaaaaaaa(138)   (Show Source): You can put this solution on YOUR website!
l = length (in feet)
w = width (in feet)
We have that, by "The length of a rectangle is 2feet less than 3times its width":

And we have that (since the area of a rectangle is calculated by multiplying length and width):

Substituting l:



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=256 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -2.33333333333333. Here's your graph:


Since we only want positive solutions, w = 3, and we can say that (based on the first statement):


Verifying, we get that .
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