Răspuns:
[tex] \frac{x}{5} = \frac{y}{12} = \frac{z}{13} = k \\ x = 5k \\ y = 12k \\ z = 13k \\ 169 {k}^{2} = 25 {k}^{2} + 144 {k}^{2} \: adevarat[/tex]
i)
30k = 90 => k = 3
x = 15
y = 36
z = 39
j)
[tex]25 {k}^{2} + 144 {k}^{2} + 169 {k}^{2} = 338 \\ 338 {k}^{2} = 338 \\ {k}^{2} = 1 \\ k = 1[/tex]
x = 5
y = 12
z = 13
k)
20k + 24k + 13k = 57
57k = 57
k = 1
x = 5
y = 12
z = 13
