a.
To write an equation using one variable to find the dimensions of the rectangle.
Given:
The perimeter of rectangle
The area of rectangle
Formula Used:
Perimeter of rectangle
Area of rectangle
Calculation:
Let the length of the rectangle
Now, the area of rectangle is:
Next, the perimeter of rectangle is:
Next, put the value of width from equation
b.
To check the discriminant and find the dimensions of rectangle.
Given:
The equation is:
Formula Used:
Quadratic formula is given as:
Calculation:
Comparing the above equation with quadratic equation of the form
The discriminant for the quadratic equation is:
Here, the discriminant is positive, hence there will be two roots for the quadratic equation. If the discriminant is negative, it means that there are no real roots for the quadratic equation.
Next, solving the quadratic equation as:
Hence, the values of
And
So, if the width of the rectangle is
Hence, the dimensions of rectangle are
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education