Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Linear Equations
4:49 minutes
Problem 9d
Textbook Question
Textbook QuestionSolve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Perimeter of a Square
The perimeter of a square is calculated by adding the lengths of all four sides, which can also be expressed as four times the length of one side. If 's' represents the length of a side, the formula is P = 4s. Understanding this concept is crucial for solving problems related to the dimensions and changes in a square's size.
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Algebraic Expressions
Algebraic expressions involve variables and constants combined using mathematical operations. In this problem, we need to set up an equation based on the relationship between the original square's perimeter and the new square's perimeter after a side length reduction. Mastery of forming and manipulating algebraic expressions is essential for finding the unknown dimensions.
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Equations and Solving for Variables
An equation is a mathematical statement that asserts the equality of two expressions. To find the dimensions of the original square, we will create an equation based on the information given and solve for the variable representing the side length. This process involves isolating the variable and applying algebraic techniques to find its value.
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