1. **Problem statement:** We have an isosceles triangle with two equal sides of length 24 cm each and a base of 14 cm. We need to find the length $x$, which is the height drawn from the bottom vertex perpendicular to the base. 2. **Formula and rules:** In an isosceles triangle, the height drawn from the vertex opposite the base bisects the base. So, the base is split into two equal segments of length $\frac{14}{2} = 7$ cm each. 3. **Using the Pythagorean theorem:** The height $x$ forms a right triangle with half the base and one of the equal sides. The sides of this right triangle are: - Hypotenuse: 24 cm (equal side) - One leg: 7 cm (half the base) - Other leg: $x$ (height) The Pythagorean theorem states: $$24^2 = x^2 + 7^2$$ 4. **Calculate $x$:** $$x^2 = 24^2 - 7^2 = 576 - 49 = 527$$ $$x = \sqrt{527}$$ 5. **Simplify the square root if possible:** 527 factors as $17 \times 31$, which are primes, so it cannot be simplified further. 6. **Final answer:** $$x = \sqrt{527} \approx 22.96 \text{ cm}$$ So, the length marked $x$ is approximately 22.96 cm.