Question

Aflati lungimea muchiei bazei piramidei patrulatere regulate care are At=21cm si ap=2cm.

Answer 1

$A_{t}= l^{2}+ 4*\frac{ a_{p}*l }{2}= l^{2} +2 a_{p}*l \\ \\ A_{t} = l^{2} +2 a_{p}*l \Leftrightarrow 21= l^{2}+4l \Leftrightarrow l^{2} +4l-21=0. \\ \\ \Delta =4 ^{2} -4*1*(-21)=16+84=100. \\ \\ l_{1,2}= \frac{ -4 \pm \sqrt{100} }{2}= \left \{ {{-8} \atop {3}} \right. . \\ l\ \textgreater \ 0 \Rightarrow l=3 ~cm.$