Question

The Floor Area of a Guest Room in the diagram is 12 x 8. If the room expanded to 40% increase, what are the new dimensions of the room?

Answer 1

First let's calculate the initial area, by multiplying the dimensions:

`\begin{gathered} A=12\cdot8 \\ A=96 \end{gathered}`

Now, let's increase this area by 40%, multiplying it by 1.4:

`A=96\cdot1.4=134.4`

Finally, to find the new dimensions, we just need to multiply them, knowing that they have the proportion of 12:8

`\begin{gathered} x\cdot y=134.4 \\ (x)/(y)=(12)/(8)\to8x=12y\to x=(12)/(8)y \\ \\ ((12)/(8)y)\cdot y=134.4 \\ y^2=134.4\cdot(8)/(12) \\ y^2=89.6 \\ y=9.466 \\ \\ x=(12)/(8)y=(12)/(8)\cdot9.466=14.199 \end{gathered}`

So the new dimensions are 14.199 and 9.466