Question

Aplicando as relações métricas nos triângulos retângulos abaixo, determine o valor da incógnita:



Por favor, me ajudem!

Answer 1

Explicação passo-a-passo:

a)

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

$\sf 6^2=12\cdot n$

$\sf 36=12\cdot n$

$\sf n=\dfrac{36}{12}$

$\sf \red{n=3}$

b)

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

$\sf b^2=(3+9)\cdot3$

$\sf b^2=12\cdot3$

$\sf b^2=36$

$\sf b=\sqrt{36}$

$\sf \red{b=6}$

c)

=> x

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

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

$\sf 4\cdot6=3x$

$\sf 24=3x$

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

$\sf \red{x=8}$

=> y

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

$\sf y^2=3\cdot(8-3)$

$\sf y^2=3\cdot5$

$\sf y^2=15$

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

d)

=> a

$\sf a=m+n$

$\sf a=2+4$

$\sf \red{a=6}$

=> h

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

$\sf h^2=2\cdot4$

$\sf h^2=8$

$\sf h=\sqrt{8}$

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

=> b

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

$\sf b^2=6\cdot4$

$\sf b^2=24$

$\sf b=\sqrt{24}$

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

=> c

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

$\sf c^2=6\cdot2$

$\sf c^2=12$

$\sf c=\sqrt{12}$

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