1. **Stating the problem:** We have a trapezoid with height $h=5$ cm, bottom base $a=5$ cm, and one slant side $c=3$ cm. There is a right angle at the intersection of height and base. 2. **Goal:** Find the length of the top base of the trapezoid. 3. **Understanding the trapezoid:** Since there is a right angle at the bottom-left corner, the height $h$ is perpendicular to the base $a$. The slant side $c=3$ cm forms a right triangle with the height and part of the base. 4. **Using the Pythagorean theorem:** Let $x$ be the horizontal segment adjacent to the height on the bottom base side, so $x$ plus the top base length equals $a=5$ cm. 5. The right triangle formed has legs $h=5$ cm and $x$, and hypotenuse $c=3$ cm. Using Pythagoras: $$c^2 = h^2 + x^2$$ $$3^2 = 5^2 + x^2$$ $$9 = 25 + x^2$$ 6. Simplify to find $x^2$: $$x^2 = 9 - 25 = -16$$ 7. Since $x^2$ is negative, this is impossible with given dimensions. This means the given dimensions do not form a right trapezoid with these side lengths. **Conclusion:** The given dimensions are inconsistent for a trapezoid with a right angle at the base-height intersection and slant side $c=3$ cm. Please check the measurements.