Question

Fie ABC un triunghi dreptunghic cu m(ung.A)=90 grade, AD perpendiculara BC, D€(BC), avand perimetrul egal cu 144 cm , iar BD/CD=9/16. Calculati: a)lungimile laturilor ABC; b)lungimea inaltimii AD c) aria triunghiului

Answer 1

BD/CD=9/16=k
BD=9K
CD=16K
BC=6K+16K=25K
AB²=BD*BC
AB²=9K*25K
AB=15K
AC²=DC*BC
AC²=16K*25K
AC=20K
BC²=AB²+AC²
BC²=225K²+400K²
BC=25K
P=AB+AC+BC
144=15K+20K+25K
144=60K
K=144/60
K=2,4
AB=2,4*15=36
AC=2,4*20=48
BC=2,4*25=60
b)
AD=AB*AC/BC
AD=36*48/60=28,8
c)
A=AB*AC/2
A=36*48/2=864