Traffic signs are regulated by the Manual on Uniform Traffic...

Name: Problem 45, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2020-04-02T06:12:58-08:00
Duration: 56 s
Channel: Surjit Tewari
Description: Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). According to this manual, if the sign below is placed on a freeway. its perimeter must be 144 inches. Also, its length is 12 inches longer than its width. Find the dimensions of this sign.

Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). According to this manual, if the sign below is placed on a freeway. its perimeter must be 144 inches. Also, its length is 12 inches longer than its width. Find the dimensions of this sign.

Key Concepts

Perimeter

Perimeter is a measure of the total length around a two-dimensional shape. In the context of a rectangle, it is calculated by adding together the lengths of all four sides or, more succinctly, using the formula 2 times the sum of the length and width. This concept is crucial when constraints are given in terms of the total boundary measurement of a figure.

Rectangular Dimensions and Relationships

For a rectangle, the length and width are the two distinct measures that define its dimensions. At times, additional relationships between these dimensions are provided—such as one side being a fixed amount longer than the other—which allows the formation of algebraic relationships. Understanding how these relationships interact with geometric formulas is essential for solving practical problems.

System of Linear Equations

When a problem provides multiple conditions involving the unknown dimensions, it naturally leads to a system of linear equations. Each condition translates into an equation, and the resulting system can be solved using various algebraic methods. Solving this system allows for the determination of the exact dimensions that satisfy all given constraints.

Substitution Method

The substitution method is a common technique for solving systems of equations, particularly when one equation can be easily rearranged to express one variable in terms of the other. This method involves substituting that expression into the second equation, thus reducing the system to a single equation with one variable. It is especially useful when dealing with problems that involve a direct relationship between dimensions.

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