SOLUTION: mr.jackson has a rectangular shaped garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden to the

Algebra ->  Rectangles -> SOLUTION: mr.jackson has a rectangular shaped garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden to the       Log On


   

Question 936218: mr.jackson has a rectangular shaped garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden to the nearest hundredth.
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
let width be x feet
length was 4 less than twice the width
length = 2*x-4
area = width x length
420 = x* (2x-4)
420 = x*2x-x*4
+420+=2x%5E2-4x
move 420 to the right
0+=+2x%5E2-4x-420
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-4x%2B-420+=+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=%28-4%29%5E2-4%2A2%2A-420=3376.

Discriminant d=3376 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+3376+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+3376+%29%29%2F2%5C2+=+15.5258390463339
x%5B2%5D+=+%28-%28-4%29-sqrt%28+3376+%29%29%2F2%5C2+=+-13.5258390463339

Quadratic expression 2x%5E2%2B-4x%2B-420 can be factored:
2x%5E2%2B-4x%2B-420+=+2%28x-15.5258390463339%29%2A%28x--13.5258390463339%29
Again, the answer is: 15.5258390463339, -13.5258390463339. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B-420+%29

x= 15.53 , -13.53
but x cannot be negative
hence width (w) = 15.53 feet
length (l) = 2*15.53-4
= 31.06-4
= 27.06 feet
length = 27.06 feet & width = 15.53 feet