Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 9

Chapter 2, Problem 9

Solve 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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Let the length of each side of the original square be represented by \(x\) inches.

The perimeter of the original square is given by \(P_{original} = 4x\).

If each side is decreased by 4 inches, the new side length is \(x - 4\), and the perimeter of the new square is \(P_{new} = 4(x - 4)\).

According to the problem, the perimeter of the new square is 10 inches more than half the perimeter of the original square, so we set up the equation: \(4(x - 4) = \frac{1}{2} \times 4x + 10\).

Simplify and solve the equation for \(x\) to find the original side length, then use that value to determine 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 the total length around it, calculated by multiplying the length of one side by 4. This concept is essential to relate the side lengths to the given perimeter values in the problem.

Algebraic Expressions and Equations

Formulating algebraic expressions to represent the original and modified side lengths and their perimeters allows setting up an equation. Solving this equation helps find the unknown side length of the original square.

Translating Word Problems into Mathematical Statements

Understanding how to convert the problem's verbal description into mathematical terms is crucial. This involves interpreting phrases like 'decreased by 4 in.' and '10 in. more than half' to form accurate equations.

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