Question

Aflati aria unui patrat care are perimetrul egal cu 8a²b²c, unde a,b,c € N*

Answer 1

[tex] \left\| \begin{array}{c} P_{\text{patrat}} = 8a^2b^2c\\ P_{\text{patrat}} = 4l \end{array} \right \Rightarrow 4l = 8a^2b^2c \Rightarrow \\ \\ \Rightarrow l = \dfrac{\not{8}a^2b^2c}{\not{4}} \Rightarrow l = 2a^2b^2c \\ \\ A_{\text{patrat}} = l^2 \Rightarrow A_{\text{patrat}} = {(2a^2b^2c)}^2 \Rightarrow \\ \\ \Rightarrow \boxed{A_{\text{patrat}} = 4a^4b^4c^2}[/tex]

Answer 2

P patrat = 4* latura
4*latura = 8a²b²c /:4 => latura = 2a²b²c

A patrat = latura*latura = latura²

A patrat = (2a²b²c)² = 4a⁴b⁴c² (cm²)