Question

A triangle has a perimeter of 65 feet. If the three sides of the triangle are n, 3n+ 5, and 3n +4, what is the length of eachside?

Answer 1

We have a triangle with perimeter P = 65ft and sides:

`\begin{gathered} l_1=n, \\ l_2=3n+5, \\ l_3=3n+4. \end{gathered}`

The perimeter of a geometrical figure is just the sum of the sides. In this case, we have:

`P=l_1+l_2+l_3._{}`

Replacing the data of the problem, we have:

`\begin{gathered} 65=(n)+(3n+5)+(3n+4) \\ 65=7n+9. \end{gathered}`

Solving for n the last equation, we get:

`\begin{gathered} 7n=65-9, \\ 7n=56, \\ n=(56)/(7)=8. \end{gathered}`

Replacing the value n = 8 in the equations for each side, we get:

`\begin{gathered} l_1=8, \\ l_2=3\cdot8+5=24+5=29, \\ l_3=3\cdot8+4=24+4=28. \end{gathered}`

Answer

The lengths of the sides are 8ft, 29ft and 28ft.