SOLUTION: Hello, I was wondering if you would be able to help me out on this problem. I'm not sure where to start: The area of the parallelogram is 108 square miles. Find it's base &

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello, I was wondering if you would be able to help me out on this problem. I'm not sure where to start: The area of the parallelogram is 108 square miles. Find it's base &       Log On


   

Question 442589: Hello,
I was wondering if you would be able to help me out on this problem. I'm not sure where to start:
The area of the parallelogram is 108 square miles. Find it's base & height.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
As you know, the area of a parallelogram = b%2Ah. It seems as though we need more information to do this. Please update your question so that I am able to help you further.
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It seems as though from your description that the base is (2x+6) as well as the height.
Knowing this, %282x%2B6%29%2A%282x%2B6%29+=+4x%5E2+%2B+24x+%2B+36+=+108
Then, 4x%5E2%2B24x+-72+=+0.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B24x%2B-72+=+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=%2824%29%5E2-4%2A4%2A-72=1728.

Discriminant d=1728 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-24%2B-sqrt%28+1728+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+1728+%29%29%2F2%5C4+=+2.19615242270663
x%5B2%5D+=+%28-%2824%29-sqrt%28+1728+%29%29%2F2%5C4+=+-8.19615242270663

Quadratic expression 4x%5E2%2B24x%2B-72 can be factored:
4x%5E2%2B24x%2B-72+=+4%28x-2.19615242270663%29%2A%28x--8.19615242270663%29
Again, the answer is: 2.19615242270663, -8.19615242270663. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B24%2Ax%2B-72+%29


Then x+=++2.1962
So 2*2.1962 + 6 = 10.393
So the base and height is 10.393 miles.
To check, 10.393 * 10.393 = 108.01 miles.
Close enough. Haha.
Let me know if you figure out if the height or base is something other than (2x+6).