Question

determine a soma de a+b+c sabendo que $\frac{a}{2} = \frac{b}{3} = \frac{c}{4} e que \\ a^{2} + b^{2} + c^{2} =261$

Answer 1

$\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}$

$3a=2b$ e $4a=2c$.

$b=\dfrac{3a}{2}$ e $c=\dfrac{4a}{2}=2a$

$a^2+b^2+c^2=261$

$a^2+\left(\dfrac{3a}{2}\right)^2+(2a)^2=261$

$a^2+\dfrac{9a^2}{4}+4a^2=261$

$4a^2+9a^2+16a^2=1044$

$29a^2=1044$

$a^2=36$

$a=6$

$b=\dfrac{3\cdot6}{2}=9$ e $c=2\cdot6=12$.

Logo, $a+b+c=6+9+12=27$.