Question

Marina brought 12 meters of fencing to construct a small playground for her daughter in her rectangular 10m by 8m backyard. She wants to decide how to place the fencing in order to construct the largest rectangular playground. Three sides of her backyard are enclosed by walls of adjacent houses and one side is connected to her house through a sliding door. How do I find the length of the other side? (Picture linked)

Answer 1

The Solution:

The length of the fencing to be constructed is 12 meters.

Given the picture below:

Note that the question says the total length of the fencing is 12 meters.

Note also that the side that is the adjacent wall of her backyard does not need fencing.

So, we shall find the length of the other side in terms of x as below:

`\begin{gathered} x+y+x=\text{total length of the fencing} \\ x+y+x=12 \end{gathered}`

Solving for y in the equation above, we get

`\begin{gathered} 2x+y=12 \\ y=12-2x \end{gathered}`

Therefore, the length of the other side in terms of x is 12-2x

Thus, the correct answer is 12 - 2x