The perimeter of a rectangle is 84 cm and its length is 6 cm less than three times its breadth. Find the LENGTH (in cm).

Half the perimeter gives length + breadth = 42. With length = $3b-6$, we get $(3b-6)+b=42$ → $4b=48$ → $b=12$, so the length is $3(12)-6=30$ cm. Check: $2(30+12)=84$. The trap 12 is the breadth and 42 is half the perimeter; 18 is $3b-6$ worked out with the wrong breadth.