Chapter 6.5, Problem 31WE

To determine

Find the perimeter using given figure.

Answer to Problem 31WE

The perimeter of the given rectangle is $\frac{44a}{15}$ .

Explanation of Solution

Given:

The given figure is

  

Calculation:

Perimeter of the rectangle is

  $\begin{array}{l}=2\left(\text{length}\right)+2\left(\text{width}\right)\\ =2\cdot \frac{4a}{5}+2\cdot \frac{2a}{3}\\ =\frac{8a}{5}+\frac{4a}{3}\end{array}$

Since the denominators are different, rewrite the fractions using their least common denominator, $15$ .

  $\begin{array}{l}=\frac{8a}{5}+\frac{4a}{3}\\ =\frac{8a\cdot 3}{5\cdot 3}+\frac{4a\cdot 5}{3\cdot 5}\\ =\frac{24a}{15}+\frac{20a}{15}\end{array}$

Useaddition/subtraction rule of fraction.

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

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

  $\begin{array}{l}=\frac{24a+20a}{15}\\ =\frac{44a}{15}\end{array}$

Hence the perimeter of the given rectangleis $\frac{44a}{15}$ .