Question

A medida de x e o perímetro do ABC, com BC = 12

Answer 1

Olá!

Primeiro vamos achar X usando proporção:

$\frac{9}{x+1} = \frac{6}{x-1} \\\\6(x+1)=9(x-1)\\\\6x+6=9x-9\\\\6x-9x=-9-6\\\\-3x=-15\\\\-x= \frac{-15}{3} \\\\-x=-5\\\\x=5$

agora vamos verificar cada um dos lados de ABC:

$AB=9+X+1\\\\AB=9+5+1\\\\AB=16\\\\ \\\\AC=6+X-1\\\\AC=6+5-1\\\\AC=10\\\\ \\\\BC = 12\\\\\\\\Logo,\\\\P=AB+AC+BC\\\\P=16+10+12\\\\P=38$

Bons Estudos! =)