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 at least $61cm$, find the minimum length of the shortest side.

Answer 1

Let us consider the problem:

longest of the shortest side be $x$ cm

therefore, length $=3$ shorter side $=3x$

and length of third side $=\left(3x-2\right)cm$

now,

perimeter $=$ sum of there side $=$ $x+3x+(3x-2)$

$=$ $x$ + $3x$+ $3x-2$

$=$ $7x-2$

Given to:

perimeter of triangle is at least $=61cm$

there fore, $\ge 61$

$7x-2\ge 61$

$7x\ge 61+2$

$7x\ge 63$

$x\ge \frac{63}{7}$

$x\ge 9$

hence the minimum leghth of the shortest side is $9cm$