Question

Aflati lungimile laturilor triunghiului ABC stiind ca perimetrul sau este de 106 cm, lungimea laturii AB este 40% din lungimea laturii AC, iar lungimea laturii AC este 80% din lungimea laturii BC.

Answer 1

Perimetrul ΔABC=AB+BC+AC
                  106=AB+BC+AC
AB=40%dinAC=>AB=40AC/100=>AB=4AC/10
AC=80%din BC=> AC=80BC/100=> AC=8BC/10
Daca AB=4AC/10 si AC= 8BC/10=> AB=(4×8BC/10)/10=> AB=32BC/10/10=> AB=32BC/10:10=> AB=32BC/10×1/10=>AB=32BC/100

106=32BC/100+BC+8BC/10 (aduc la acelasi numitor)
106=32BC/100+100BC/100+8×10BC/100
106=32BC/100+100BC/100+80BC/100
106=212BC/100=> BC=106×100=212BC=> 10600=212BC=> BC=10600/212=>BC=50
Daca BC=50=> AB=32×50/100=>AB=1600/100=>AB=16
Daca BC=50=> AC=8×50/10=> AC=400/10=> AC=40