Question

Calcule os valores desconhecidos em cada caso​

Answer 1

Explicação passo-a-passo:

Relações métricas no triângulo retângulo

a)

$\sf b^2=a\cdot m$

$\sf y^2=25\cdot16$

$\sf y^2=400$

$\sf y=\sqrt{400}$

$\sf \red{y=20}$

b)

$\sf c^2=a\cdot n$

$\sf y^2=9\cdot4$

$\sf y^2=36$

$\sf y=\sqrt{36}$

$\sf \red{y=6}$

c)

=> Valor de x

$\sf b^2=a\cdot m$

$\sf (2\sqrt{6})^2=x\cdot3$

$\sf 4\cdot6=3x$

$\sf 24=3x$

$\sf x=\dfrac{24}{3}$

$\sf \red{x=8}$

=> Valor de y

Pelo Teorema de Pitágoras:

$\sf y^2+3^2=(2\sqrt{6})^2$

$\sf y^2+9=4\cdot6$

$\sf y^2+9=24$

$\sf y^2=24-9$

$\sf y^2=15$

$\sf \red{y=\sqrt{15}}$

d)

=> Valor de "a"

$\sf a=m+n$

$\sf a=2+4$

$\sf \red{a=6}$

=> Valor de b

$\sf b^2=a\cdot m$

$\sf b^2=6\cdot4$

$\sf b^2=24$

$\sf b=\sqrt{24}$

$\sf \red{b=2\sqrt{6}}$

=> Valor de c

$\sf c^2=a\cdot n$

$\sf c^2=6\cdot2$

$\sf c^2=12$

$\sf c=\sqrt{12}$

$\sf \red{b=2\sqrt{3}}$

=> Valor de h

$\sf h^2=m\cdot n$

$\sf h^2=2\cdot4$

$\sf h^2=8$

$\sf h=\sqrt{8}$

$\sf \red{h=2\sqrt{2}}$