Răspuns:
Explicație pas cu pas:
[tex]\dfrac{a}{3} =\dfrac{b}{4} =\dfrac{c}{7}~~=>~ (\dfrac{a}{3})^2 =(\dfrac{b}{4})^2=(\dfrac{c}{7})^2~~=>~\dfrac{a^2}{9} =\dfrac{b^2}{16} =\dfrac{c^2}{49}=\dfrac{a^2+b^2}{9+16} ~~=>~\dfrac{c^2}{49}=\dfrac{100}{25}~=>~\dfrac{c^2}{49}=4[/tex]
Deci c²=49·4, deci c=√(49·4)=7·2=14. Atunci
[tex]\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{14}{7}=2,[/tex] deci a=3·2=6, b=4·2=8.
Răspuns: a=6, b=8, c=14.
Ex12. Fie a, b sunt laturile dreptunghiului, ⇒ P=2·(a+b)=120, ⇒a+b=60.
[tex]\dfrac{a}{5}=\dfrac{b}{7}=\dfrac{a+b}{5+7}=\dfrac{60}{12}=5[/tex]
Deci, a=5·5=25, iar b=7·5=35.
Verificare: P=2·(25+35)=2·60=120cm corect
Aria=a·b=25·35=875cm²
