Question

aria unui romb este egala cu 120 cm2, iar diferenta lungimilor diagonalelor este de 14cm aflati latura rombului.

Answer 1

$A= \frac{ d_{1}* d_{2} }{2} \\ 120= \frac{ d_{1}* d_{2} }{2} \\ 240= d_{1}* d_{2} \\ si:14= d_{1}- d_{2} \\ \left \{ {{ d_{1} =14+ d_{2} } \atop {(14+ d_{2}) d_{2} =240}} \right. \\ \left \{ {{ d_{1} =14+ d_{2} } \atop { d^2_{2}+14 d_{2}-240 =0}} \right. \\ \left \{ {{ d_{1} = d_{2}+14 } \atop { d_{2} =10}} \right. \\ \left \{ {{ d_{1} =24} \atop { d_{2} =10}} \right.$
$a^{2}= \frac{ d^2_{1} }{2}+ \frac{ d^2_{2} }{2} \\ a^{2}=12^2+5^2=169 \\ a=13 cm$