1. **State the problem:** We are given the area of an equilateral triangle as $\frac{70}{3}$ and need to find the length of its side. 2. **Formula for the area of an equilateral triangle:** $$\text{Area} = \frac{\sqrt{3}}{4} s^2$$ where $s$ is the side length. 3. **Set up the equation:** $$\frac{\sqrt{3}}{4} s^2 = \frac{70}{3}$$ 4. **Solve for $s^2$:** Multiply both sides by 4: $$\cancel{\frac{\sqrt{3}}{4}} \times 4 s^2 = \frac{70}{3} \times 4$$ which simplifies to: $$\sqrt{3} s^2 = \frac{280}{3}$$ 5. **Divide both sides by $\sqrt{3}$:** $$s^2 = \frac{280}{3 \sqrt{3}}$$ 6. **Rationalize the denominator:** $$s^2 = \frac{280}{3 \sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{280 \sqrt{3}}{3 \times 3} = \frac{280 \sqrt{3}}{9}$$ 7. **Take the square root of both sides:** $$s = \sqrt{\frac{280 \sqrt{3}}{9}} = \frac{\sqrt{280 \sqrt{3}}}{3}$$ 8. **Simplify inside the square root:** Note that $280 = 4 \times 70$, so: $$\sqrt{280 \sqrt{3}} = \sqrt{4 \times 70 \sqrt{3}} = 2 \sqrt{70 \sqrt{3}}$$ 9. **Final expression for $s$:** $$s = \frac{2 \sqrt{70 \sqrt{3}}}{3}$$ This is the exact side length of the equilateral triangle with area $\frac{70}{3}$. **Answer:** $$s = \frac{2 \sqrt{70 \sqrt{3}}}{3}$$