SOLUTION: what is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters

Question 223710: what is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
What is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters.

Step 1. Let w be the width

Step 2. Let 2w be the length.

Step 3. Let w+1 be the width increased by one meter.

Step 4. Let 2w-3 be the length diminished by three meters.

Step 5. The Area A=(w+1)(2w-3)=12 since the area will be 12 meters with these changed dimensions.

Step 6. Solving the equation in Step 5 will lead to a quadratic equation as follows:

Subtract 12 from both sides of the equation

Step 7. To solve, use the quadratic formula given as

where a=2, b=-1, and c=-15.

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=121 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -2.5. Here's your graph:

Selecting the positive solution given as , then . Check area A with width 3+1=4 and length 2w-3=3. So the area with these dimensions is 12 as given by the problem statement.

Step 8. ANSWER: The length is 6 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
RELATED QUESTIONS
turn into the variable the length of a rectangle is twice its width if the width is... (answered by drj)

The length of a rectangle is 3 times its width. If the width is diminished by one meter... (answered by ankor@dixie-net.com)

the length of a rectangle is 3 times it width. If the width is diminished by 1 meter and... (answered by Deina)

The length of a rectangle is four times its width. If the width is diminished by 2m and... (answered by josgarithmetic)

the width of a rectangle is 15m shorter than its length. if its length were increased by... (answered by KMST)

the length of a rectangle is 3 times its width. if the width is diminished by 1 meter and (answered by JBarnum)

if the perimeter of a rectangle is 112 meter, and the length is one meter shorter than... (answered by asuar010)

The length of a rectangle is 4 inches greater than twice its width. If the length and... (answered by ReadingBoosters)

If each dimension of a room is increased one meter, the area is increased by 51 meters ;... (answered by ikleyn)