Final answer:
The measures of each side of the triangle are 21 inches, 27 inches, and 36 inches.
Step-by-step explanation:
To find the measures of each side of the triangle, we need to use the given ratio and the perimeter of the triangle. Let's assume the ratio is 7x:9x:12x, where x is a constant. The sum of the ratio is 7x+9x+12x=84. Simplifying, we get 28x=84. Dividing both sides by 28, we find x=3. Therefore, the measures of each side are 7x=21 inches, 9x=27 inches, and 12x=36 inches.