Question

Mateo used 14 meters of fence for a rectangular pen alongside his house. He only needs to fence three sides such that the length is 1 meter more than triple the width. He decides to put the longer side length along the house as shown.What is the area of the pen?

Answer 1

Let's begin by listing out the information given to us:

Mateo used 14m of fence total

He fences 3 sides

Length is 1 more than three times the width:

`l=1+3w`

The sum of the length of one side & width of 2 sides. We proceed to calculate for the length and width as shown below:

`\begin{gathered} 14=l+w \\ But,l=1+3w \\ \Rightarrow14=1+3w+w \\ \Rightarrow14=1+4w \\ 14-1=4w\Rightarrow13=4w \\ 4w=13 \\ w=(13)/(4)=3(1)/(4) \\ w=3(1)/(4)m \\ \\ l=1+3w\Rightarrow l=1+3(3\frac{1}{4_{}}) \\ l=1+9(3)/(4)=10(3)/(4) \\ l=10(3)/(4)m \end{gathered}`

The Area of the rectangle is given by:

`\begin{gathered} A=l\cdot w=10(3)/(4)\cdot3(1)/(4) \\ A=(43)/(4)\cdot(13)/(4)=(559)/(16) \\ A=34(15)/(16)=34.9375\approx35m \\ A=35m \end{gathered}`