1. **State the problem:** We need to find the base and height of a triangle where the base is 4 cm less than twice its height, and the area is 60 cm². 2. **Define variables:** Let the height be $h$ cm. 3. **Express the base in terms of height:** The base $b = 2h - 4$ cm. 4. **Use the area formula for a triangle:** Area $= \frac{1}{2} \times \text{base} \times \text{height}$. 5. **Set up the equation:** $$60 = \frac{1}{2} \times (2h - 4) \times h$$ 6. **Simplify the equation:** $$60 = \frac{1}{2} (2h^2 - 4h) = h^2 - 2h$$ 7. **Rewrite as a quadratic equation:** $$h^2 - 2h - 60 = 0$$ 8. **Solve the quadratic equation:** Using the quadratic formula $h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a=1$, $b=-2$, $c=-60$: $$h = \frac{2 \pm \sqrt{(-2)^2 - 4 \times 1 \times (-60)}}{2} = \frac{2 \pm \sqrt{4 + 240}}{2} = \frac{2 \pm \sqrt{244}}{2}$$ 9. **Calculate the square root:** $$\sqrt{244} = \sqrt{4 \times 61} = 2\sqrt{61}$$ 10. **Find the two possible values for $h$:** $$h = \frac{2 \pm 2\sqrt{61}}{2} = 1 \pm \sqrt{61}$$ 11. **Choose the positive value for height:** $$h = 1 + \sqrt{61} \approx 1 + 7.81 = 8.81 \text{ cm}$$ 12. **Find the base:** $$b = 2h - 4 = 2(8.81) - 4 = 17.62 - 4 = 13.62 \text{ cm}$$ **Final answer:** The height is approximately $8.81$ cm and the base is approximately $13.62$ cm.