Question

The longest side of a triangle is $3$ times the shortest side and the third side is $2$ cm shorter than the longest side. If the perimeter of the triangle is at least $61$ cm, find the minimum length in cm. of the shortest side.

Answer 1

Let the length of the shortest side of the triangle be $x$ cm.
Then length of the longest side $=3x$ cm.
Thus the length of the third side $=(3x-2)$ cm.
Since the perimeter of the triangle is at least $61$ cm,
$x+3x+(3x-2)$ $\ge$ $61$
$\Rightarrow 7x-2\ge 61$
$\Rightarrow 7x\ge 61+2$
$\Rightarrow 7x\ge 63$

$\Rightarrow x\ge 9$
Thus the minimum length of the shortest side is $9$ cm.