SOLUTION: The area of a garden is 160 m2. Suppose the length of the length of the garden is 3 m more than twice its width. What is the length of the garden?

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Question 984419: The area of a garden is 160 m2. Suppose the length of the length of the garden is 3 m more than twice its width. What is the length of the garden?
Found 2 solutions by solver91311, Timnewman:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the width. Then represents the length. Since the area of a rectangle is the length times the width,



Which is to say



Solve the quadratic for and then calculate

John

My calculator said it, I believe it, that settles it

Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
Hi dear,
Let L=lengh
w=width
If L*w=160----(1)
and L=3+2w---(2)
put (2) in (1)
(3+2w)w=160
2w²+3w-160=0
solving quadratic equation,
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-160+=+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=%283%29%5E2-4%2A2%2A-160=1289.

Discriminant d=1289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+1289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+1289+%29%29%2F2%5C2+=+8.22566153550812
x%5B2%5D+=+%28-%283%29-sqrt%28+1289+%29%29%2F2%5C2+=+-9.72566153550812

Quadratic expression 2x%5E2%2B3x%2B-160 can be factored:
2x%5E2%2B3x%2B-160+=+2%28x-8.22566153550812%29%2A%28x--9.72566153550812%29
Again, the answer is: 8.22566153550812, -9.72566153550812. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-160+%29

Since w=8 aproximately,
put w=8 in in equ 2
there L=3+2*8
L=19m
the lenght is 19m
hope this helps;