Question

Se considera nr. naturale a,b,c astfel incat numerele: 2a+3b ; 5b+3c si 3a+4c sunt direct proportionale cu 22. 29 respectiv 27. Arati ca a,b, si c sunt lungimile laturilor unui triunghi dreptunghic.

Answer 1

(2a+3b)/22 = (5b+3c)/29 = (3a+4c)/27

din (2a+3b)/22 =(5b+3c)/29 ⇒ 29(2a+3b) = 22(5b+3c) ⇒  58a+87b=110b+66c    58a-23b=66c    a = (23b+66c)/58     din  (2a+3b)/22 =(3a+4c)/27 ⇒ 54a+81b =66a+88c ⇒12a=81b-88c  ⇒ a=(81b-88c)/12;  deci, (23b+66c)/58 = (81b-88c)/12 ⇒⇒ (23b+66c)/29 = (81b-88c) /6 ⇒ 138b + 396c = 2349b - 2552c ⇒ 2948c = 2211b     ]÷737 ⇒4c = 3b ⇒ c=3b/4 din a = (81b-88c)/12 ⇒a=(81b-66b)/12 =15b/12 a=5b/4 ⇒a²=25b²/16=c²+b² (9b²/16 +b² = 25b²/16) ⇒ in Δ dreptunghic a² = b² + c²