SOLUTION: One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.

Algebra.Com
Question 229271: One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.

Step 1. Area A is the width times length for a rectangle.

Step 2. Let w be the width.

Step 3. Let w+4 be the length.

Step 4. Then, A=w(w+4)=140 since area is 140 square feet.

Subtract 140 to both sides to get the following





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



where a=1, b=4, and c=-140

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=576 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 10, -14. Here's your graph:



Selecting the positive answer gives w=10 and w+4=14. Note the area is 140 square feet using these two dimensions.

Step 6. ANSWER: The width is 10 feet and the length is 14 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
RELATED QUESTIONS

one side of a rectangular patio is 4 feet longer than the other. if the area of the... (answered by user_dude2008)
One side of a rectangular patio is 6 feet longer than the other. If the area of the patio (answered by edjones)
The area of a rectangular patio is 96 square feet. The length of the patio is the width (answered by JulietG)
The area of a patio is 90 square feet. The length of the patio is 1 foot longer than the... (answered by jim_thompson5910)
Introductory Algebra ISBN 0321279212 Chapter 6.7 Solve this application. Quadratic... (answered by tutor_paul)
A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the... (answered by jim_thompson5910)
The area of a square patio is 196 square feet. How long is each side of the​... (answered by Alan3354)
Emma wants to start with a square patio and experiment with the sides to see how changing (answered by gonzo)
the length of a rectangular patio is three-time its width. The area of the patio is 432... (answered by josgarithmetic)