Question

21. No A da figura a seguir, DE //BC. Nessas condições, determine: 6 F a) A medida x. b) 0 perimetro do AABC, com BC = 12. x + 1 *- 1​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\sf\dfrac{x+1+9}{9}=\dfrac{6+x-1}{6}\\\\\sf\dfrac{x+10}{9}=\dfrac{x+5}{6}\\\\\sf 9x+45=6x+60\\\sf 9x-6x=60-45\\\sf 3x=15\\\sf x=\dfrac{15}{3}\\\\\sf x=5\checkmark\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\sf AB= x+10=5+10=15\\\sf AC= x+5=5+5=10\\\sf 2p\longrightarrow per\acute imetro\,do\,\triangle ABC\\\sf 2p=AB+AC+BC\\\sf 2p=15+10+12\\\sf 2p=37\end{array}}$