1. **Problem statement:** We have a rhombus with an area of 32 cm². One diagonal is given as 8 cm, and the other diagonal is labeled as $b$ cm. We need to find the value of $x$ where $b = x$ cm. 2. **Formula for the area of a rhombus:** The area $A$ of a rhombus can be calculated using the formula: $$A = \frac{d_1 \times d_2}{2}$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Given values:** - $A = 32$ cm² - $d_1 = 8$ cm - $d_2 = b = x$ cm (unknown) 4. **Substitute the known values into the formula:** $$32 = \frac{8 \times x}{2}$$ 5. **Solve for $x$:** Multiply both sides by 2: $$64 = 8x$$ Divide both sides by 8: $$x = \frac{64}{8} = 8$$ 6. **Answer:** The value of $x$ is 8 cm.