Question

The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.

Answer 1

Let the shortest side of the triangle be x cm.
Then, the longest side will be 3x and the third side will be 3x − 2.

$$\begin{gathered} \therefore \mathrm{Perimeter}\mathrm{of}\mathrm{the}\mathrm{triangle}\ge 61 \\ \Rightarrow x+3x+3x-2\ge 61 \\ \Rightarrow 7x\ge 61+2 \\ \Rightarrow x\ge 9(\mathrm{Dividing}\mathrm{throughout}\mathrm{by}7) \\ \mathrm{Hence},\mathrm{the}\mathrm{minumum}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{shortest}\mathrm{side}\mathrm{is}9\mathrm{cm}. \end{gathered}$$