Let's begin by identifying key information given to us:
The perimeter of triangle = 65 ft
The perimeter of a triangle is calculated using the formula:
[tex]\begin{gathered} P=a+b+c \\ \text{In this case, it is given as:} \\ P=l+m+n \end{gathered}[/tex]
The triangles has the following sides:
[tex]\begin{gathered} l=\frac{1}{3}m \\ m=m \\ n=l+m-15\Rightarrow n=\frac{1}{3}m+m-15\Rightarrow n=\frac{4}{3}m-15 \\ n=\frac{4}{3}m-15 \\ We\text{ will substitute this into the formula for perimeter. We have:} \\ P=l+m+n \\ 65=\frac{1}{3}m+m+\frac{4}{3}m-15 \\ 65=\frac{8}{3}m-15 \\ 65+15=\frac{8}{3}m \\ 80=\frac{8}{3}m\Rightarrow\frac{8}{3}m=80 \\ \frac{8}{3}m=80 \\ 8m=80\times3 \\ m=\frac{80\times3}{8}=30 \\ m=30ft \\ l=\frac{1}{3}m\Rightarrow l=\frac{1}{3}\times30=10 \\ l=10ft \\ n=l+m-15\Rightarrow10+30-15=40-15=25 \\ n=25ft \\ \\ \therefore m=30ft,l=10ft,n=25ft \end{gathered}[/tex]
The system of equations that represents this situation is l = 1/3m, n = l + m -15 and m
