Answer
Length of longest side is less than $21$ cm
Work Step by Step
It is given that the length of the sides of the triangle are in ratio $5 : 6 : 7$. .
Let the sides of the triangle be $5k$, $6k$, $7k$ cm respectively.
The perimeter of the triangle is given to be less than $54$ cm.
$5k + 6k + 7k < 54$
$18k < 54$
$k < 3$
$7k < 21$
Therefore, the length of the longest side must be less than $21$ cm.
