SOLUTION: the length of a rectangle is 12 meters longer than half the width. the area of the rectangle is 90 square meters. find the dimensions of the rectangle.

Question 221567: the length of a rectangle is 12 meters longer than half the width. the area of the rectangle is 90 square meters. find the dimensions of the rectangle.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 12 meters longer than half the width. The area of the rectangle is 90 square meters. Find the dimensions of the rectangle.

Step 1. Let w be the width.

Step 2. Let be the length.

Step 3. Area

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

Multiply 2 to both sides to get rid of denominator

Subtract 180 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=24, and c=-180

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=1296 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -30. Here's your graph:

With , then . Area A=6*15=90 which is a true statement.

Step 6. ANSWER: The dimensions of a rectangle are 6 meters and 15 meters.

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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