SOLUTION: One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.

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Question 229271: One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.

Step 1. Area A is the width times length for a rectangle.

Step 2. Let w be the width.

Step 3. Let w+4 be the length.

Step 4. Then, A=w(w+4)=140 since area is 140 square feet.

Subtract 140 to both sides to get the following

w%5E2%2B4w-140=140-140

w%5E2%2B4w-140=0

Step 5. To solve, use the quadratic formula given as

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

where a=1, b=4, and c=-140

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-140+=+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=%284%29%5E2-4%2A1%2A-140=576.

Discriminant d=576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+576+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+10
x%5B2%5D+=+%28-%284%29-sqrt%28+576+%29%29%2F2%5C1+=+-14

Quadratic expression 1x%5E2%2B4x%2B-140 can be factored:
1x%5E2%2B4x%2B-140+=+1%28x-10%29%2A%28x--14%29
Again, the answer is: 10, -14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-140+%29



Selecting the positive answer gives w=10 and w+4=14. Note the area is 140 square feet using these two dimensions.

Step 6. ANSWER: The width is 10 feet and the length is 14 feet.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J