Final answer:
The base of the triangular-shaped rug is 8 yards.
Step-by-step explanation:
To find the base of the triangular-shaped rug, we can use the formula for the area of a triangle, which is 1/2 × base × height. In this case, the area is given as 12 square yards and the height is given as 3 yards. Plugging in these values into the formula:
12 = 1/2 × base × 3
Multiplying both sides of the equation by 2 and dividing by 3, we get:
base = 8 yards