Question

Equations to find the triangle sides and steps on finding it! image contains more information

Answer 1

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:

`\begin{gathered} P=a+b+c \\ \text{In this case, it is given as:} \\ P=l+m+n \end{gathered}`

The triangles has the following sides:

`\begin{gathered} l=(1)/(3)m \\ m=m \\ n=l+m-15\Rightarrow n=(1)/(3)m+m-15\Rightarrow n=(4)/(3)m-15 \\ n=(4)/(3)m-15 \\ We\text{ will substitute this into the formula for perimeter. We have:} \\ P=l+m+n \\ 65=(1)/(3)m+m+(4)/(3)m-15 \\ 65=(8)/(3)m-15 \\ 65+15=(8)/(3)m \\ 80=(8)/(3)m\Rightarrow(8)/(3)m=80 \\ (8)/(3)m=80 \\ 8m=80*3 \\ m=(80*3)/(8)=30 \\ m=30ft \\ l=(1)/(3)m\Rightarrow l=(1)/(3)*30=10 \\ l=10ft \\ n=l+m-15\Rightarrow10+30-15=40-15=25 \\ n=25ft \\ \\ \therefore m=30ft,l=10ft,n=25ft \end{gathered}`

The system of equations that represents this situation is l = 1/3m, n = l + m -15 and m