SOLUTION: solve algebraically using only one variable: the length of a rectangle is two more than twice its width. if the area of the rectangle is 84, find the length and the width.

Question 228533: solve algebraically using only one variable: the length of a rectangle is two more than twice its width. if the area of the rectangle is 84, find the length and the width.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Solve algebraically using only one variable: the length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and the width.
Step 1. Area A of a rectangle is A=width times the length

Step 2. Let w be the width.

Step 3. Let 2w+2 be the length since the length it's two more than twice its width.

Step 4. Then, .

Step 5. Solving yields the following steps:

Subtract 84 from both sides of the equation

Step 6. To solve, use the quadratic equation given as

where a=2, b=2, and c=-84.

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=676 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -7. Here's your graph:

Selecting the positive solution

and and the A=6*14=84 which is a true statement.

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

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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