The lengths of the sides of a triangle are in the ratio 5:6:7. Describe the length of the longest side if the perimeter is less than 54 cm.

Answer 1

Let the common ratio be represented by $x$. Then, the lengths of the sides are $5x$, $6x$, and $7x$ for some positive value of $x$, so the perimeter is $5x + 6x + 7x = 18x$. Setting this expression less than 54, we get $18x < 54$, which implies $x < 3$. Therefore, the longest side is $\boxed{7x < 21\text{ cm}}$.