SOLUTION: a rectangle is 4 cm longer than it is wide, and it area is 117 cm squared. find its dimensions.

Question 224584: a rectangle is 4 cm longer than it is wide, and it area is 117 cm squared. find its dimensions.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
A rectangle is 4 cm longer than it is wide, and it area is 117 cm squared. Find its dimensions.

Step 1. Let w be the width

Step 2. Let w+4 be the length

Step 3. Let Area A=w(w+4)=117 where the area is the product of the length and the width.

Step 4. Then where we subtracted 117 from both sides of the equation to get a quadratic equation.

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

where a=1, b=4 and c=-117

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=484 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, -13. Here's your graph:

Selecting the positive solution we have w=9 then w+4=13 and A=9*13=117 which is a true statement.

Step 6. ANSWER: The width is 9 cm and the length is 13 cm.

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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV
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