Question

In triunghiul ABC , m(A)=90 , se stie ca inaltimea AD=12 cm si DB pe DC = 9 pe 16.Determinati perimetrul triunghiului.

Answer 1

DB/DC=9/16=> DC=16BD/9. IN TR ABC aplicam th inaltimii => AD²=BD*DC =>144=BD*16 BD/9 =>BD²=144*9/16 =>BD=9 =>DC=16.  => BC=25 . FIE TR dreptunghic ADC=> CONF TH PITAAGORA AC²=AD²+DC²=144+256=400=>AC=20. In tr drptunghic ADB=> conf th Pitagor² AB²=AD²+DB²=144+81=225=>AB=15 =>P=AB+BC+AC=60 CM