U trokutu A B C ABC A B C b b b 14 c m 14\ \mathrm{cm} 14 cm a a a 4 c m 4\ \mathrm{cm} 4 cm c c c 140 c m 140\ \mathrm{cm} 140 cm A B C ABC A B C
Rješenje Prvo rješenje.
b = a − 14 ⟹ a = b + 14 b=a-14\implies a=b+14 b = a − 14 ⟹ a = b + 14 b = c + 4 ⟹ c = b − 4 b=c+4\implies c=b-4 b = c + 4 ⟹ c = b − 4 2 a + 2 b + 2 c = 140 2 ( a + b + c ) = 140 a + b + c = 70 b + 14 + b + b − 4 = 70 3 b + 10 = 70 3 b = 70 − 10 3 b = 60 b = 20 c m \begin{aligned} 2a+2b+2c&=140\\ 2(a+b+c)&=140\\ a+b+c&=70\\ b+14+b+b-4&=70\\ 3b+10&=70\\ 3b&=70-10\\ 3b&=60\\ b&=20\ \mathrm{cm} \end{aligned} 2 a + 2 b + 2 c 2 ( a + b + c ) a + b + c b + 14 + b + b − 4 3 b + 10 3 b 3 b b = 140 = 140 = 70 = 70 = 70 = 70 − 10 = 60 = 20 cm a = b + 14 = 20 + 14 = 34 c m a=b+14=20+14=34\ \mathrm{cm} a = b + 14 = 20 + 14 = 34 cm c = b − 4 = 20 − 4 = 16 c m c=b-4=20-4=16\ \mathrm{cm} c = b − 4 = 20 − 4 = 16 cm Drugo rješenje.
b = a − 14 ⟹ a = b + 14 b=a-14\implies a=b+14 b = a − 14 ⟹ a = b + 14 b = c + 4 ⟹ c = b − 4 b=c+4\implies c=b-4 b = c + 4 ⟹ c = b − 4
Oznake na skici:
Iz označene skice slijedi zaključak:
b + 14 + b + 14 + b + b + b − 4 + b − 4 = 140 b+14+b+14+b+b+b-4+b-4=140 b + 14 + b + 14 + b + b + b − 4 + b − 4 = 140 6 b + 20 = 140 6b+20=140 6 b + 20 = 140 b = 20 c m b=20\ \mathrm{cm} b = 20 cm a = b + 14 = 20 + 14 = 34 c m a=b+14=20+14=34\ \mathrm{cm} a = b + 14 = 20 + 14 = 34 cm c = a − 4 = 20 − 4 = 16 c m c=a-4=20-4=16\ \mathrm{cm} c = a − 4 = 20 − 4 = 16 cm 
