1. **State the problem:** We are given the area of a rectangular parking lot as $\alpha^2 - 25$ and told the length is longer than the width. We need to factor the area expression to find possible dimensions and then find the width if the length is 105 yards. 2. **Recall the formula for area of a rectangle:** $$\text{Area} = \text{Length} \times \text{Width}$$ 3. **Factor the expression $\alpha^2 - 25$:** This is a difference of squares since $25 = 5^2$. $$\alpha^2 - 25 = (\alpha - 5)(\alpha + 5)$$ 4. **Interpret the factors as dimensions:** Possible dimensions are $\alpha - 5$ and $\alpha + 5$. Since length is longer, length $= \alpha + 5$ and width $= \alpha - 5$. 5. **Given length is 105 yards:** $$\alpha + 5 = 105$$ Solve for $\alpha$: $$\alpha = 105 - 5 = 100$$ 6. **Find the width:** $$\text{Width} = \alpha - 5 = 100 - 5 = 95$$ **Final answer:** The width of the parking lot is 95 yards.