Question

The longest side of a triangle is three times the shortest side and the 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 length of the shortest side be x

Then,the length of the longest side and thrid side of the triangle are 3x and 3x-2 respectively.

According to question,

perimeter of triangle $\ge 61\Rightarrow x+3x-2+3x\ge 61\Rightarrow 7x\ge 61+2\Rightarrow 7x\ge 63\Rightarrow x\ge \frac{63}{7}\Rightarrow x\ge 9\therefore \text{The minimum length of the shortest side is 9 cm.}$