1. **State the problem:** We have a compound L-shaped figure made of two rectangles. The total area is given as 75 cm². We need to find the value of $x$, the width of the upper rectangle. 2. **Identify the dimensions:** - The taller left rectangle has height 6 cm and width 3 cm (since the lower horizontal segment is 3 cm wide). - The upper rectangle has height 3 cm and width $x$ cm. 3. **Write the formula for area:** The total area is the sum of the areas of the two rectangles: $$\text{Area} = \text{Area}_1 + \text{Area}_2$$ where $$\text{Area}_1 = 6 \times 3 = 18$$ $$\text{Area}_2 = 3 \times x = 3x$$ 4. **Set up the equation:** $$18 + 3x = 75$$ 5. **Solve for $x$:** $$3x = 75 - 18$$ $$3x = 57$$ $$\cancel{3}x = \frac{57}{\cancel{3}}$$ $$x = 19$$ 6. **Answer:** The value of $x$ is 19 cm.