Question

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

• A. $7cm$
• B. $8cm$
• C. $9cm$
• D. $10cm$

Answer 1

Answer: (C)

Let the shortest side be $\times cm$.
Then, according to the given condition,
Longest side $=3xcm$ and third side $=(3x-2)cm$
Now, perimeter of triangle $\ge 61$ i.e., sum of all sides $\ge 61$
$\Rightarrow x+3x+3x-2\ge 61$
$\Rightarrow 2+7x-2\ge 61+2$
$\Rightarrow 7x\ge 63$
$\Rightarrow \frac{7x}{7}\ge \frac{63}{7}$
$\Rightarrow x\ge 9$
$\therefore$ Minimum length of the shortest side is $9cm$.