Question

Calcule os valores desconhecidos:

Answer 1

Explicação passo-a-passo:

a)

• Valor de "a"

$\sf a=m+n$

$\sf a=20+30$

$\sf \red{a=50}$

• Valor de "h"

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

$\sf h^2=20\cdot30$

$\sf h^2=600$

$\sf h=\sqrt{600}$

$\sf \red{h=10\sqrt{6}}$

• Valor de "b"

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

$\sf b^2=50\cdot30$

$\sf b^2=1500$

$\sf b=\sqrt{1500}$

$\sf \red{b=10\sqrt{15}}$

• Valor de "c"

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

$\sf c^2=50\cdot20$

$\sf c^2=1000$

$\sf c=\sqrt{1000}$

$\sf \red{c=10\sqrt{10}}$

b)

• Valor de "a"

$\sf a=m+n$

$\sf a=5+10$

$\sf \red{a=15}$

• Valor de "h"

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

$\sf h^2=5\cdot10$

$\sf h^2=50$

$\sf h=\sqrt{50}$

$\sf \red{h=5\sqrt{2}}$

• Valor de "b"

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

$\sf b^2=15\cdot10$

$\sf b^2=150$

$\sf b=\sqrt{150}$

$\sf \red{b=5\sqrt{6}}$

• Valor de "c"

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

$\sf c^2=15\cdot5$

$\sf c^2=75$

$\sf c=\sqrt{75}$

$\sf \red{c=5\sqrt{3}}$

c)

• Valor de "n"

$\sf a=m+n$

$\sf 70=30+n$

$\sf n=70-30$

$\sf \red{n=40}$

• Valor de "h"

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

$\sf h^2=30\cdot40$

$\sf h^2=1200$

$\sf h=\sqrt{1200}$

$\sf \red{h=20\sqrt{6}}$

• Valor de "b"

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

$\sf b^2=70\cdot40$

$\sf b^2=2800$

$\sf b=\sqrt{2800}$

$\sf \red{b=20\sqrt{7}}$

• Valor de "c"

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

$\sf c^2=70\cdot30$

$\sf c^2=2100$

$\sf c=\sqrt{2100}$

$\sf \red{c=10\sqrt{21}}$

d)

• Valor de "m"

$\sf a=m+n$

$\sf 30=m+20$

$\sf m=30-20$

$\sf \red{m=10}$

• Valor de "h"

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

$\sf h^2=10\cdot20$

$\sf h^2=200$

$\sf h=\sqrt{200}$

$\sf \red{h=10\sqrt{2}}$

• Valor de "b"

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

$\sf b^2=30\cdot20$

$\sf b^2=600$

$\sf b=\sqrt{600}$

$\sf \red{b=10\sqrt{6}}$

• Valor de "c"

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

$\sf c^2=30\cdot10$

$\sf c^2=300$

$\sf c=\sqrt{300}$

$\sf \red{c=10\sqrt{3}}$

e)

Pelo Teorema de Pitágoras:

$\sf x^2=3^2+4^2$

$\sf x^2=9+16$

$\sf x^2=25$

$\sf x=\sqrt{25}$

$\sf \red{x=5}$