Question

20. A rectangular plot of land has a perimeterthat does not exceed 36.4 meters. If thelength of the plot is 3 times the width, whatis the length of the rectangular plot?

Answer 1

The length does not exceed 13.65 meters.

Step-by-step explanation

Let the width of the plot of land be x.

This means that the length of the plot of land is:

`\begin{gathered} 3\cdot x \\ \Rightarrow3x \end{gathered}`

The plot of land is rectangular. The perimeter of a rectangle is given as:

`P=2(l+w)`

The perimeter of the land does not exceed 36.4 meters, which means that:

`P\le36.4`

This implies that:

`\begin{gathered} 2(l+w)\le36.4 \\ \Rightarrow2(3x+x)\le36.4 \\ \Rightarrow2(4x)\le36.4 \\ 8x\le36.4 \end{gathered}`

Hence, we can solve for x:

`\begin{gathered} \Rightarrow x\le(36.4)/(8) \\ x\le4.55\text{ meters} \end{gathered}`

Recall that length is:

`l=3\cdot x`

Therefore, the length of the plot of land has the values:

`\begin{gathered} l\le3\cdot4.55 \\ l\le13.65\text{ meters} \end{gathered}`

In other words, the length does not exceed 13.65 meters.