Set 9: Quadratic Equations

Choice A is correct. Choice A is the correct answer. 1. Setup: Let $x$ be the width (perpendicular to river). The length (parallel to river) is $100- 2 x$. 2. Area Function: $A(x) = x(100 - 2 x) = -2 x^2 + 100 x$. 3. Maximize: Find the vertex $x = -b/2 a = -100 / (2(-2)) = 25$. 4. Calculate Area: $A(25) = 25(100 - 50) = 25(50) = 1250$ sq meters. Choice B is incorrect because it assumes a square with 4 sides ($25\times 25$ is wrong perimeter). Choice C is incorrect. Choice D is incorrect.