Chapter 4 Quadratic Functions and Factoring - 4.1 Graph Quadratic Functions in Standard Form - 4.1 Exercises - Problem Solving - Page 243: 61

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We have a formula of the area: $A=wL$ Formula of the length parallel to the beach: $P=2w+L$ Find: $w=-\frac{b}{2a}=-\frac{P}{2(-2)}=\frac{P}{4}$ Thus, $P=2w+L\\ \rightarrow L=P-2w\\ \rightarrow L=P-\frac{P}{4}=\frac{P}{2}$ Then, $A=\frac{P}{4}.\frac{P}{2}=\frac{P^2}{8}$