Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 777: 58

a) 15.81 cm by 47.43 cm b) 126.48 cm

a) $x^2+(3x)^2=50^2$ $10x^2=2500$ $10x^2/10=2500/10$ $x^2=250$ $\sqrt {x^2} = \sqrt {250}$ $x=±15.81$ We want only the positive value of $x$ since we are talking about a distance. $x=15.81$ $15.81*3=47.43$ b) $15.81+47.43=63.24$ $63.24*2=126.48$