SOLUTION: A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 yeards. What is the length and width of the parking lot

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Question 215233: A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 yeards. What is the length and width of the parking lot
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 yeards. What is the length and width of the parking lot.

Step 1. Let w be the width and w+3 is the length

Step 2. Let Area A=w%28w%2B3%29=w%5E2%2B3w=180 or w%5E2%2B3w-180=0
where w%5E2%2B3w-180=%28x-12%29%28x%2B15%29=0 where x=12 and x=-15.

Step 3. We can now also use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=3 and c=-180.

Also, please ignore the graph since the scaling is not properly set.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-180+=+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%2A1%2A-180=729.

Discriminant d=729 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+729+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+729+%29%29%2F2%5C1+=+12
x%5B2%5D+=+%28-%283%29-sqrt%28+729+%29%29%2F2%5C1+=+-15

Quadratic expression 1x%5E2%2B3x%2B-180 can be factored:
1x%5E2%2B3x%2B-180+=+1%28x-12%29%2A%28x--15%29
Again, the answer is: 12, -15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-180+%29



Select x=12 for positive lengths. Then x+3=15

Step 4. ANSWER. The dimensions are 12 for the width and 15 for the length of the parking lot.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J