Chapter 10 - Radical Functions and Equations - 10.3 - Solving Radical Equations - Monitoring Progress - Page 563: 14

$\approx 5~feet$

$$P=2\pi\sqrt{\frac{L}{32}}$$ Substitute $P=2.5$ and solve for $L$: $$2.5=2\pi\sqrt{\frac{L}{32}}$$ $$2.5^2=4\pi^2\frac{L}{32}$$ $$L=\frac{2.5^2\cdot 32}{4\pi^2}=\frac{6.25\cdot 32}{4\pi^2}\approx 5~feet$$