Verified answer

Ratio 3:5:4

let ratio be x = 3x,4x,5x

[tex]Semi \: perimeter = \frac{3 + 5 + 4}{2} \\ \\ = \frac{12}{2} = 6 \\ \\ x = \frac{450}{52} \\ \\ x = \frac{72}{5} [/tex]

[tex]3x = 3 \times 75 = 225 \\ \\ 5x = 5 \times 75 = 375 \\ \\ 4x = 4x \times 75 = 240[/tex]

[tex] \sqrt{450(450 - 225)(450 - 375)(450 - 240)} [/tex]

[tex] = \sqrt{450 \times 225 \times 75 \times 150} \\ \\ = 33750 \: units[/tex]

[tex]Ratio \: \: 3:5:4 \\ \\ let \: \: ratio \: \: be \: \: x \: \: = 3x,4x,5x \\ \\ \begin{gathered}Semi \: perimeter = \frac{3 + 5 + 4}{2} \\ \\ = \frac{12}{2} = 6 \\ \\ x = \frac{450}{52} \\ \\ x = \frac{72}{5} \end{gathered} \\ \\\begin{gathered}3x = 3 \times 75 = 225 \\ \\ 5x = 5 \times 75 = 375 \\ \\ 4x = 4x \times 75 = 240\end{gathered} \\ \\ \sqrt{450(450 - 225)(450 - 375)(450 - 240)} \\ \\ \begin{gathered} = \sqrt{450 \times 225 \times 75 \times 150} \\ \\=33750\:units\end{gathered}.[/tex]