To Find: The dimensions of the cardboard for which the volume of the boxes produced by
both methods will be the same.
The dimensions of the cardboard is
Given:
Length of the cardboard piece is
The manufacturer cut out either
Explanation:
On the left is a rectangular piece of cardboard, and on the right is a cardboard box:
Here, the longer side is
Consider
The Volume of the Cardboard is:
Here
(Which is the cardboard height)
And
(Which is the cardboard width)
And
(Which is the cardboard length)
Blue line length is
Red line Length is
Green line length is
Represent the volume of the box using one variable:
What system of equations can you write? Which method can you use to solve the system?
So, the volume of the cardboard box is
The dimensions for the cardboard box are to be determined if it weighs the same when cut into
Find the value of
So, the system of equations can be written as:
Method used: quadratic formula Using the quadratic formula:
Substitute
It is not possible to cut
So, the dimensions of the cardboard is
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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- 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