SOLUTION: Find the perimeter of the rectangle with length of 3x, width of 2x-1 and area of 45m^2

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Question 992424: Find the perimeter of the rectangle with length of 3x, width of 2x-1 and area of 45m^2
Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
Hi dear,
If lenght L=3x----(1)
and width w=2x-1--(2)
Annd,
L*w=45----(3)
Put equ 1 and 2 in 3
3x(2x-1)=45
6x²-3x-45=0
Solve the quadratic equation as follows
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-3x%2B-45+=+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=%28-3%29%5E2-4%2A6%2A-45=1089.

Discriminant d=1089 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+1089+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+1089+%29%29%2F2%5C6+=+3
x%5B2%5D+=+%28-%28-3%29-sqrt%28+1089+%29%29%2F2%5C6+=+-2.5

Quadratic expression 6x%5E2%2B-3x%2B-45 can be factored:
6x%5E2%2B-3x%2B-45+=+6%28x-3%29%2A%28x--2.5%29
Again, the answer is: 3, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-3%2Ax%2B-45+%29

Since x=3 or -2.5
L=3(3)=9m
Or
L=3(-2.5)=-7.5m
Now,w=2(3)-1=5m
Or,
w=2(-2.5)-1=-6
Ingnore those once having the nagative sign
Then,
Perimeter p=2(L+w)
p=2(9+5)m
p=28m
The perimeter of the figure is 28meters.
HOPE THIS HELPS?