Chapter 6.5, Problem 34WE

To determine

Find the perimeter using given figure.

Answer to Problem 34WE

The perimeter of the given rectangle is $\frac{14x}{3}$ .

Explanation of Solution

Given:

The given figure is

  

Calculation:

Perimeter of the given rectangle $=$ sum of all sides

From the diagram

  

  $\begin{array}{l}=\frac{3x}{4}+\frac{x}{6}+\frac{x}{4}+\frac{3x}{4}+\frac{x}{4}+\frac{x}{6}+\frac{3x}{4}+\frac{x}{6}+\frac{x}{4}+\frac{3x}{4}+\frac{x}{4}+\frac{x}{6}\\ =4\cdot \frac{3x}{4}+4\cdot \frac{x}{6}+4\cdot \frac{x}{4}\\ =3x+\frac{2x}{3}+x\\ =4x+\frac{2x}{3}\end{array}$

Since the denominators are different, rewrite the fractions using their least common denominator, $3$ .

  $\begin{array}{l}=\frac{4\cdot 3x}{3}+\frac{2x}{3}\\ =\frac{12x}{3}+\frac{2x}{3}\end{array}$

Use addition/subtraction rule of fraction.

  $\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm b}{c}$

To add/subtract fractions with the same denominator, add/subtract their numerators and write the result over the common denominator.

  $\begin{array}{l}=\frac{12x+2x}{3}\\ =\frac{14x}{3}\end{array}$

Hence the perimeter of the given rectangle is $\frac{14x}{3}$ .