First let's calculate the initial area, by multiplying the dimensions:
[tex]\begin{gathered} A=12\cdot8 \\ A=96 \end{gathered}[/tex]Now, let's increase this area by 40%, multiplying it by 1.4:
[tex]A=96\cdot1.4=134.4[/tex]Finally, to find the new dimensions, we just need to multiply them, knowing that they have the proportion of 12:8
[tex]\begin{gathered} x\cdot y=134.4 \\ \frac{x}{y}=\frac{12}{8}\to8x=12y\to x=\frac{12}{8}y \\ \\ (\frac{12}{8}y)\cdot y=134.4 \\ y^2=134.4\cdot\frac{8}{12} \\ y^2=89.6 \\ y=9.466 \\ \\ x=\frac{12}{8}y=\frac{12}{8}\cdot9.466=14.199 \end{gathered}[/tex]So the new dimensions are 14.199 and 9.466
