Question

Sabendo que o triângulo ABC é isosceles de base BC, determine, em centímetros, o perímetro do triângulo.

Answer 1

A medida do perímetro do triângulo isósceles é 18cm

Perímetro do triângulo

Para calcular o perímetro do triângulo, devemos descobrir os valores de seus lados

Calculamos a dAB, dBC e dCA, somamos esses valores encontrados e teremos o Perímetro

Perímetro é a soma de todos os lados de um polígono

Simbolizado por 2P

$2P=dAB+dBC+dCA\\\\\\Devemos~antes~descobrir~o~valor~de~~"x"\\\\\\(3x-10)+(2x+4)+(x+4)=0\\\\\\3x+2x+x-10+4+4=0\\\\\\6x-2=0\\\\\\6x=2\\\\\\x=\dfrac{2}{6} \\\\\\Valor~de~x=\dfrac{1}{3} \\\\\\Substituimos,~~em:\\\\\\dAB=3x-10\\\\\\dAB=3.\dfrac{1}{3} -10\\\\\\\\dAB=\dfrac{3}{3} -10\\\\\\dAB=1-10\\\\\\dAB=-9\\\\\\dAB=9cm$

Não existe distância negativa, logo dAB=9cm

$dBC=2x+4\\\\\\dBC=2. \dfrac{1}{3} +4\\\\\\dBC=\dfrac{2}{3} +4\\\\\\dBC=\dfrac{2+12}{3} \\\\\\dBC=\dfrac{14}{3} \\\\\\\\dCA=x+4\\\\\\dCA=\dfrac{1}{3}+4\\\\\\dCA=\dfrac{1+12}{3} \\\\\\dCA=\dfrac{13}{3} \\\\\\2P=dAB+dBC+dCA\\\\\\2P=9+\dfrac{14}{3} +\dfrac{13}{3} \\\\\\2P=\dfrac{27+14+13}{3} \\\\\\2P=\dfrac{54}{3} \\\\\\2P=~18cm$

Para saber mais acesse o link abaixo

Perímetro

brainly.com.br/tarefa/47775811