1. **Problem statement:** We have an isosceles triangle with two equal sides of length 14 cm and a base of 24 cm. We need to find the length $x$ of the altitude (height) drawn from the vertex opposite the base to the base, forming a right angle. 2. **Formula and rules:** In an isosceles triangle, the altitude to the base bisects the base into two equal segments. So each segment of the base is $\frac{24}{2} = 12$ cm. 3. **Using the Pythagorean theorem:** The altitude $x$ forms a right triangle with half the base (12 cm) and the equal side (14 cm). The Pythagorean theorem states: $$x^2 + 12^2 = 14^2$$ 4. **Calculate $x$:** $$x^2 = 14^2 - 12^2 = 196 - 144 = 52$$ $$x = \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}$$ 5. **Final answer:** The length marked $x$ is $2\sqrt{13}$ cm, approximately 7.21 cm.