Question

The longest side of a triangle is thrice the shortest side and the third side is 5 cm longer than the shortest side. If the perimeter of the triangle is atleast 60 cm then the minimum length of the shortest side is

• A. 11.0
• B. 011
• C. 11.00
• D. 11

Answer 1

Answer: (A), (B), (C), (D)

Let the length of shortest side be $x$ cm.
Then longest side length $=3x$ and the third side length $=x+5$
$\therefore$ Perimeter $=x+3x+x+5=5x+5$
Given that perimeter $\ge 60$
$\Rightarrow 5x+5\ge 60$
$\Rightarrow 5x\ge 55$
$\Rightarrow x\ge 11$

Hence, the minimum length of the shortest side is $11cm$