Solution

\[ \begin{aligned} \text{Perimeter of the square} & = 40 \, \text{m} \\ \text{Length of the rectangle } {\color{green} (l)}& = x \\ \text{Breadth of the rectangle} & =\frac{1}{3} \text{ of length} \\ \\ & =\frac{1}{3} \times x \\ \\ \color{green} b & =\frac{x}{3} \\ \\ \end{aligned} \] \[ \begin{aligned} \text{Perimeter of the rectangle} & = \left(\frac{2}{5} \times 40 \right) - 2.4\\ \\ 2 \times (l + b)& = \left(\frac{2}{\cancelto{1}{5}} \times \cancelto{8}{40} \right) - 2.4\\ \\ 2 \times \left( x + \frac{x}{3} \right) & = (2 \times 8) - 2.4 \\ \\ 2 \times \left(\frac{3x +x}{3} \right) & = 16 - 2.4 \\ \\ 2 \times \frac{4x}{3} & = 13.6 \\ \\ \frac{8x}{3} & = 13.6 \\ \\ x & = 13.6 \times \frac{3}{8}\\ \\ x & = \frac{\cancelto{17}{136}}{10} \times \frac{3}{\cancelto{1}{8}}\\ \\ x & = \frac{51}{10} \\ \\ x & = 5.1 \, m \\ \\ \color{green}Length & = \color{green}5.1 \, m \\ \\ b & = \frac{x}{3} \\ \\ &= \frac{5.1}{3} \\ \\ & = 1.7 \\ \\ \color{green}Breadth & = \color{green}1.7 \, m \\ \\ \end{aligned} \]

Answer Length = \( \color{red} 5.1 \, \text{m} \), Breadth = \( \color{red} 1.7 \, \text{m} \)