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:

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

The Area of the rectangle is given by:

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