Question

Calculaţi dimensiunile dreptunghiului cu aria A si perimetrul P,dacă:
a.)A=18,25cm ^2 si P=19,6cm
b.)A=110cm^2 si P=32 radical din 2
cm c.)A=14/27 cm^2 si P=13/9 cm
d.)A=32cm^2 si P=36 cm

Answer 1

[tex]\texttt{La fiecare din punctele a), b), c) si d), } \\ \texttt{aria o decompunem convenabil in doi factori} \\ a) \\ A = 18,25~cm^2 = 2,5~cm \times 7,3~cm \\ P = 2(2,5~cm + 7,3~cm) = 2 \times 9,8~cm = 19,6 cm \\ \Longrightarrow ~~ L= 7,3~cm ~~~si ~~~ l = 2,5~cm\\ b) \\ A=110cm^2 = 2 \times 5 \times 11 = 5\sqrt{2}~cm \times 11\sqrt{2}~cm \\P=2(5\sqrt{2}~cm + 11\sqrt{2}~cm)=2 \times 16\sqrt{2} = 32\sqrt{2}~cm \\ \Longrightarrow ~~ L= 11\sqrt{2}~cm ~~~si ~~~ l = 5\sqrt{2}~cm[/tex]

[tex]\displaystyle c) \\ \text{Punctul c) pare a avea o greseala. Il voi rezolva considerand: } P= \frac{26}{9} \\ A= \frac{14}{27}~cm^2 = \frac{2}{3}~cm \times \frac{7}{9}~cm \\ \\ P=2\left( \frac{2}{3}+ \frac{7}{9}\right)= 2\left( \frac{6}{9}+ \frac{7}{9}\right)= 2\times \frac{13}{9}=\frac{26}{9} \\ \\ \Longrightarrow ~~ L= \frac{2}{3}~cm ~~~si ~~~ l = \frac{7}{9}~cm [/tex]

[tex]d)\\A=32cm^2 = 2~cm \times 16~cm \\ P= 2(2~cm + 16~cm)=2 \times 18 = 36~cm \\ \Longrightarrow ~~ L= 18~cm ~~~si ~~~ l = 2~cm[/tex]