Răspuns:
a)
[tex]P=12\\A=9[/tex]
b)
[tex]P=20\\A=25[/tex]
Explicație pas cu pas:
a)
[tex]A(0,~2)\\B(\sqrt{5},~0)[/tex]
[tex]AB=\sqrt{(0-\sqrt{5})^2 + (2-0)^2}\\AB=\sqrt{\sqrt{5}^2+2^2}\\AB=\sqrt{5+4}\\AB=\sqrt{9}\\AB=3\\\\P=AB\cdot4\\P=3\cdot4\\P=12\\\\A=AB^2\\A=3^2\\A=9[/tex]
b)
[tex]A(4,~1)\\C(9,~6)\\[/tex]
[tex]AC=\sqrt{(4-9)^2+(1-6)^2}\\AC=\sqrt{(-5)^2+(-5)^2}\\AC=\sqrt{25+25}\\AC=\sqrt{25\cdot2}\\AC=5\sqrt{2}[/tex]
[tex]\text{Fie $AB$ latura p\u{a}tratului.}[/tex]
[tex]\left \substack{AC~\text{diagonal\u{a}}\\AC=5\sqrt{2}} \right \} \Rightarrow AB=\frac{\text{diagonala}}{\sqrt{2}}\\\Rightarrow AB=\frac{5\sqrt{2}}{\sqrt{2}}\\\Rightarrow AB=5[/tex]
[tex]P=AB\cdot4\\P=5\cdot4\\P=20[/tex]
[tex]A=AB^2\\A=5^2\\A=25[/tex]
