#### Answer

$\frac{142}{45}$, $3\frac{7}{45}$, or $3.155...$.

#### Work Step by Step

The formula for a rectangle's perimeter is $P=2l+2w$. The length is $\frac{4}{5}$m, and the width is $\frac{7}{9}$m. To solve, insert the values into the formula, as shown below.
$P=2(\frac{4}{5})+2(\frac{7}{9})$
$P=\frac{8}{5}+\frac{14}{9}$
$P=\frac{72}{45}+\frac{70}{45}$
$P=\frac{142}{45}$
It can also be written as $3\frac{7}{45}$ or $3.155...$.