Question

14. What is the perimeter of the figure below? Show your work.

Answer 1

Check the picture below.

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) ~\hfill AB=√((~~ 4- 0~~)^2 + (~~ 0- 4~~)^2) \\\\\\ ~\hfill AB=√(( 4)^2 + ( -4)^2) \implies \boxed{AB=√( 32 )}`

`B(\stackrel{x_1}{4}~,~\stackrel{y_1}{0})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill BC=√((~~ 5- 4~~)^2 + (~~ 4- 0~~)^2) \\\\\\ ~\hfill BC=√(( 1)^2 + ( 4)^2) \implies \boxed{BC=√( 17 )}`

`C(\stackrel{x_1}{5}~,~\stackrel{y_1}{4})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{4}) ~\hfill CA=√((~~ 0- 5~~)^2 + (~~ 4- 4~~)^2) \\\\\\ ~\hfill CA=√(( -5)^2 + (0)^2) \implies CA=√( 25 )\implies \boxed{CA=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{√(32)~~ + ~~√(17)~~ + ~~5 ~~} \approx ~~ \text{\LARGE 14.78}`