Question

Fie triunghiul dreptunghic ABC cu m(A) = 90° si D proiectia ortogonala a varfului A pe ipotenuza :
a) Daca BD = 54 cm si CD = 36 cm, calculati AB si AC.
b) Daca BD = 5√2 cm si AB = 10 cm, calculati CD si AC.
c) Daca CD = √15 cm si AC = 3√10 cm, calculati BC si AB.

Answer 1

a)BC=90 cm
=>t.catetei : AB²=BD×BC <=>AB²=54×90 =>AB=18√15 cm
=>t.catetei : AC²=CD×BC <=>AC²=36×90 =>AC=18√10 cm

b)t.catetei : AB²=BD×BC <=>100=5√2×BC =>BC=10√2 cm
=>CD=10√2-5√2 =>CD=5√2
t.Pit. : 100+AC²=200 =>AC²=100 =>AC=10 cm

c)t.catetei : AC²=DC×BC =>90=√15×BC =>BC=6√15 cm
t.Pit. : AB²+90=540 =>AB²=450 =>AB=15√2 cm