Final answer:
The radius of the large circle is 12 units, as determined by comparing the ratio of the areas between the large and small circles and using the area formula for a circle, A = πr².
Step-by-step explanation:
The area of a large circle is 144 times the area of a small circle. Given that the radius of the small circle is 1 unit, we can find the length of the radius of the large circle by setting up a ratio. The area of a circle is given by the formula A = πr², where A is the area and r is the radius. For the small circle with radius r = 1, the area is π(1²) = π. For the large circle, if we let its radius be R, the area would be πR².
Setting up the ratio, we have πR² = 144×(π×1²), which simplifies to R² = 144. Taking the square root of both sides, we find R = √144 = 12. Therefore, the length of the radius of the large circle is 12 units.
However, if we want the length to the nearest tenth, it is already an exact integer and thus remains 12.0 to one decimal place.