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 atleast $61\, cm$, then minimum length of the shortest side is

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

Answer 1

Answer: (C)

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