1. **State the problem:** We are given the area of a rectangular pool deck as $3x^2 + 11x - 20$ square meters and the width as $x + 5$ meters. We need to find the length. 2. **Formula used:** The area $A$ of a rectangle is given by $A = \text{length} \times \text{width}$. 3. **Set up the equation:** Let the length be $L$. Then: $$3x^2 + 11x - 20 = L \times (x + 5)$$ 4. **Find the length by dividing the area by the width:** $$L = \frac{3x^2 + 11x - 20}{x + 5}$$ 5. **Factor the numerator:** $$3x^2 + 11x - 20 = (3x - 4)(x + 5)$$ 6. **Substitute the factorization:** $$L = \frac{(3x - 4)(x + 5)}{x + 5}$$ 7. **Cancel the common factor $(x + 5)$:** $$L = \frac{(3x - 4)\cancel{(x + 5)}}{\cancel{x + 5}} = 3x - 4$$ 8. **Final answer:** The length of the pool deck is $3x - 4$ meters.