[tex]A=350cm^{2}\\ \\ A= \frac{d_{1} \cdot d_{2}}{2} \\ \\ \frac{d_{1} \cdot d_{2}}{2} =350 \\ \\ d_{1} \cdot d_{2}=700 \\ \\ \frac{d_{1}}{d_{2}} = \frac{4}{7} \\ \\ d_{1}= \frac{4d_{2}}{7} \\ \\ \frac{4d_{2}}{7} \cdot d_{2} =700 \\ \\ d_{2}^{2}= \frac{700 \cdot7}{4} \\ \\d_{2}=35 \\ \\ d_{1}= \frac{4d_{2}}{7}= \frac{4 \cdot35}{7} =20[/tex]
Diagonalele se intretaie in segmente egale. Diagonalele formeaza 4 triunghiuri dreptunghice cu catetele egale cu diag /2 si ipotenuza care de fapt este latura rombului
[tex] ip^{2} = (\frac{d_{1} }{2})^{2} + (\frac{d_{2} }{2})^{2} \\ \\ ip= \sqrt{(\frac{d_{1} }{2})^{2} + (\frac{d_{2} }{2})^{2}} = \sqrt{ (\frac{20 }{2})^{2} + (\frac{35}{2})^{2}} \\ \\ ip=latura= \sqrt{100+17,5^{2} } = \sqrt{406,25} =20,155[/tex]
