Answer Not Defined
Let the length of the rectangular prism be \(x\) cm. \[ \therefore \text{Width} = \frac{x}{3} \text{ cm}, \quad \text{Height} = \frac{x}{5} \text{ cm} \] \[ \therefore x \times \frac{x}{3} \times \frac{x}{5} = 14400 \Rightarrow \frac{x^3}{15} = 14400 \Rightarrow x^3 = 14400 \times 15 = 216000 \Rightarrow x = 60 \] \[ \therefore \text{Length} = 60 cm, \quad \text{Width} = \frac{60}{3} = 20 cm, \quad \text{Height} = \frac{60}{5} = 12 cm \] \[ \therefore \text{Total surface area} = 2(60 \times 20 + 20 \times 12 + 12 \times 60) \text{ cm}^2 = 2(1200 + 240 + 720) \text{ cm}^2 = 2 \times 2160 \text{ cm}^2 = 4320 \text{ cm}^2 \] \[ \therefore \text{The total surface area of the rectangular prism is } 4320 \text{ square cm}. \]
Let the length of the rectangular prism be \(x\) cm. \[ \therefore \text{Width} = \frac{x}{3} \text{ cm}, \quad \text{Height} = \frac{x}{5} \text{ cm} \] \[ \therefore x \times \frac{x}{3} \times \frac{x}{5} = 14400 \Rightarrow \frac{x^3}{15} = 14400 \Rightarrow x^3 = 14400 \times 15 = 216000 \Rightarrow x = 60 \] \[ \therefore \text{Length} = 60 cm, \quad \text{Width} = \frac{60}{3} = 20 cm, \quad \text{Height} = \frac{60}{5} = 12 cm \] \[ \therefore \text{Total surface area} = 2(60 \times 20 + 20 \times 12 + 12 \times 60) \text{ cm}^2 = 2(1200 + 240 + 720) \text{ cm}^2 = 2 \times 2160 \text{ cm}^2 = 4320 \text{ cm}^2 \] \[ \therefore \text{The total surface area of the rectangular prism is } 4320 \text{ square cm}. \]