Ch. 1 - Equations and Inequalities

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

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Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 31

Chapter 2, Problem 31

Dimensions of a Square What is the length of the side of a square if its area and perimeter are numerically equal?

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Let the length of the side of the square be \(x\). Since it is a square, all sides are equal in length.

Write the formula for the area of the square: \(\text{Area} = x^2\).

Write the formula for the perimeter of the square: \(\text{Perimeter} = 4x\).

Set the area equal to the perimeter because the problem states they are numerically equal: \(x^2 = 4x\).

Solve the equation \(x^2 = 4x\) by bringing all terms to one side: \(x^2 - 4x = 0\), then factor: \(x(x - 4) = 0\). Find the values of \(x\) that satisfy this equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Area of a Square

The area of a square is calculated by squaring the length of one of its sides (Area = side²). This represents the total space enclosed within the square's boundaries.

Perimeter of a Square

The perimeter of a square is the total length around the square, found by multiplying the length of one side by four (Perimeter = 4 × side). It measures the boundary length.

Setting up and Solving Equations

To find the side length when area and perimeter are equal, set the expressions for area and perimeter equal to each other (side² = 4 × side) and solve the resulting equation for the side length.

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