SOLUTION: the width of a rectangle is 5ft less than the length. the area is 6ft^2

Question 221566: the width of a rectangle is 5ft less than the length. the area is 6ft^2

Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The width of a rectangle is 5 ft less than the length. The area is 6ft^2

I assume you want to find the dimensions of the rectangle.

Step 1. Let L be the length.

Step 2. Let be the width.

Step 3. Area

Step 4. Solving A in Step 3 yields the following steps.

Subtract 6 from both sides to get a quadratic equation

Step 5. To solve equation in Step 5, use the quadratic formula given below

where a=1, b=-5, and c=-6

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -1. Here's your graph:

Using the positive solution , then . Area A=6*1=6 which is a true statement.

Step 6. ANSWER: The dimensions of a rectangle are 6 feet and 1 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

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