[tex]\displaystyle\\
\text{In dreptunghiul ABC lungimea AB, latimea BC si diagonala AC}\\
\text{formeaza triunghiul dreptunghic ABC in care:}\\
\sphericalangle B = 90^o\\
AB = 12~cm = \text{cateta}\\
AC = 13~cm = \text{ipotenuza}\\
BC = ?~cm = \text{cateta}\\\\
a)\\
BC = \sqrt{AC^2-AB^2}= \sqrt{13^2-12^2}=\sqrt{169-144}= \sqrt{25}= \boxed{\bf 5~cm}\\\\
b)\\
P = 2(L+l)=2(AB+BC)=2(12+5)=2\times 17 = \boxed{\bf 34~cm}\\\\
c)\\
A = L \times l = AB \times BC = 12 \times 5 = \boxed{\bf 60~cm^2}
[/tex]
