Question

ajutati maaaaa ex 4.....​

Answer 1

$AB=\sqrt{(16+8)^2+(16-20)^2}=\sqrt{576+16} =\sqrt{592} =4\sqrt{37} \\\\AC=\sqrt{(12+8)^2+(-8-20)^2} =\sqrt{400+784}= 4\sqrt{74} \\\\BC=\sqrt{(12-16)^2+(-8-16)^2}=4\sqrt{37}$

Observam ca daca le ridicam la patrat pe fiecare in parte obtinem:

AB²=592

BC²=592

AC²=1184

AC²=AB²+BC²⇒ ΔABC dreptunghic in B, ipotenuza fiind AC

Deci

$A_{ABC}=\frac{AB\times BC}{2} =\frac{4\sqrt{37}\times 4\sqrt{37} }{2} =8\times 37=296cm^2\\\\P_{ABC}=4\sqrt{37}+4\sqrt{37}+4\sqrt{74} =8\sqrt{37}+4\sqrt{74}=4\sqrt{37}(2+\sqrt{2} )cm$