Dimensions of rectangular garden given area and wire length

Let the longer side be $x\text{ m}$ and shorter side be $y\text{ m}$. Area $x \cdot y = 180 \implies y = \frac{180}{x}$. Fencing 3 sides leaving one longer side unfenced: $x + 2y = 39 \quad \text{or} \quad x + 2\left(\frac{180}{x}\right) = 39$ $x^2 + 360 = 39x$ $x^2 - 39x + 360 = 0$ $(x - 24)(x - 15) = 0$ $x = 24$ or $x = 15$. Since $x$ is the longer side ($x > y$), if $x = 24\text{ m}$, then $y = 7.5\text{ m}$. If $x = 15\text{ m}$, $y = 12\text{ m}$ (not strictly longer if unfenced side is 15). Dimensions: length $= 24\text{ m}$, breadth $= 7.5\text{ m}$ (or $15\text{ m} \times 12\text{ m}$).