Question

Latura unui patrat este 0,5din latimea unui dreptunghi ,iar perimetrul patratului este o cincime din perimetrul dreptunghiului . Sa se afle aria patratului stiind ca aria dreptunghiului este egala cu 16m la a doua .

Answer 1

$n \to latura \ patratului \\\\ n-0,5 \ din \ l \\\\ \ \textless \ =\ \textgreater \ n=\frac{\not 5}{\not 10}*l \ \textless \ =\ \textgreater \ n=\frac{1}{2}*l \longrightarrow \underline{n=\frac{l}{2}} \\\\\\ P_p=\frac{1}{5} \ din \ P_d \ \textless \ =\ \textgreater \ P_p=\frac{1}{5}*P_d \longrightarrow P_p=\frac{P_d}{5} \\\\\\\not4 * \frac{l}{\not2}=\frac{2L+2l}{5} \\\\ 2l=\frac{2L+2l}{5} \\\\ 10l=2L+2l \\\\ 10l-2l=2L \\\\ 8l=2L \ \ \ |:2 \\\\\\ \underline{4l=L} \\\\\\ A_d=L*l \\\\ 16=4l*l \ \ \ |:4 \\\\ 4=l^2 \\\\ 2^2=l^2 \\\\ \boxed{l=2m}$

$n- \frac{l}{2}=\frac{\not 2}{\not 2} \longrightarrow \boxed{n=1m} \\\\\\ \hbox{Aria patratului este:} \\\\ A_p=n^2 = 1^2 \\\\\ \boxed{\boxed{A_p=1m^2}}$