Răspuns:
55,2 cm
Explicație pas cu pas:
[tex]AB²=BC²-AC² = {25}^{2} - {20}^{2} = 225=>AB = 15 \: cm[/tex]
[tex]AR = \frac{AB \times AC}{BC} = \frac{15 \times 20}{25}=>AR = 12 \: cm[/tex]
[tex]AQRP \: dreptunghi \:(RQ||PA,RP||QA)= > AR = QP = 12 \: cm\:(diagonale)[/tex]
[tex]RC²=AC²-AR²=20²-12²=256=>RC=16cm[/tex]
[tex]RC²=QC×AC =>QC= \frac{16^{2} }{20} = \frac{64}{5} \: cm[/tex]
[tex]BR²=AB²-AR²=15²-12²=81=>BR=9 \: cm[/tex]
[tex]BR²=BP×AB=>BP= \frac{ {9}^{2} }{15} = \frac{27}{5} \: cm[/tex]
[tex]perimetrul(BCQP) = 25 + \frac{64}{5} + 12 + \frac{27}{5} = 37 + \frac{91}{5} = 55.2 \: cm[/tex]
