Question

uma escada de 12 metros de comprimento esta apoiada sob um muro . a base da escada esta distante do muro da cerca de 8 metros . determine a altura do muro .

Answer 1

      Lara,

      Veja esboço do sistema
           
             P                                   A escada, o piso e a parede forma o triangulo
             |                                     retângulo PSQ onde
             |                                     PQ = escada = 12 metros
             |                                     SQ = distancia escada-muro = 8 metros
             |                                     PS = altura muro = ??
             |              
             S             Q                    Pelo Teorema de Pitágoras
                                                    (PQ)^2 = (PS)^2 + (SQ)^2
                                                      (12)^2 = (PS)^2 + (8)^2
                                                          144 = (PS)^2 + 64
                                                     (PS)^2 = 144 - 64
                                                                 = 80
                                                           PS = √80
                                                                 = 4√5
                                                                 = 4(2,2361)
                                                                 = 8,94
           ALTURA DO MURO = 9 METROS   (8.94 arredondado)

Answer 2

Resposta:

aproximadamente 9 metros

Explicação passo-a-passo:

Teorema de Pitágoras: a² = b² + c²

$12^{2} =x^{2} +8^{2} \\144=x^{2} +64\\-x^{2} =64-144\\-x^{2} =-80\:\times(-1)\\x^{2} =80\\\sqrt{x^{2} } =\sqrt{80} \\x=4\sqrt{5}$

x = 4 × 2,24

x ≅ 8,96

Esse muro tem aproximadamente 9 metros