Chapter 1.5, Problem 23WE

To determine

To choose: A variable for the length of the side of a square and to write an equation which represents the given perimeter of the square in terms of the variable for length

Answer to Problem 23WE

The variable for length of side of the square is a

The equation representing the perimeter of the square is $4a=116$

Explanation of Solution

Given Information:

A square with perimeter 116 m.

Formula Used:

A square has four sides and their values are equal to one another as shown in Figure 1.

The following approach is used to obtain the equation of the perimeter of the square

a. Choosing a variable for the length of side of the square

b. The perimeter of a rectangle in general is the sum of its sides. Here, a square is to be considered and it has equal sides. Thus, perimeter, P can be expressed as,

  $P=4\times \text{ length of one side}$

The variable chosen can be assigned in the above expression to get the equation of perimeter of square.

Calculation:

Based on the square shown in Figure 1, the length of side can be represented using the variable “ a ”

  

Using this variable in the expression for perimeter of the square, the equation of the perimeter can be rewritten as,

  $\begin{array}{c}P=4\times a\\ =4a\end{array}$

Here, perimeter is given as P = 116 m. Substituting this value in the above equation gives,

  $4a=116$