Question

Si, a/2=b/5=c/3 y a^2 + b^2 + c^2 =152​

Answer 1

☆ RESOLUCIÓN:

$\frac{a}{2} = \frac{b}{5} = \frac{c}{3} = k$

$→ \boxed{a = 2k}$

$→ \boxed{b = 5k}$

$→ \boxed{c = 3k}$

$⇒ {a}^{2} + {b}^{2} + {c}^{2} = 152 \\ (2k) {}^{2} + (5k) {}^{2} + (3k) {}^{2} = 152 \\ 4 {k}^{2} + 25 {k}^{2} + 9 {k}^{2} = 152 \\ 38 {k}^{2} = 152 \\ {k}^{2} = \frac{152}{38} \\ {k}^{2} = 4 \\ k = \sqrt{4} \\  \boxed{k = 2}$

$→ a = 2k = 2 \times 2 = \boxed{4}$

$→ b = 5k = 5 \times 2 = \boxed{10}$

$→c = 3k = 3 \times 2 =  \boxed{6}$

☆ RESPUESTA:

$\boxed{a = 4}$

$\boxed{b = 10}$

$\boxed{c = 6}$