Question

In trapezul ABCD avem: N=prAB C si D prAD N. Folositi datele din figura data pt a calcula lungimile: NB NC ND si BC.

Answer 1

   
[tex]\displaystyle\\ \text{Din desen se vede ca }~BC = AD ~\Longrightarrow~\text{Trapezul este isoscel.}\\\\ NB = \frac{AB-CD}{2}= \frac{102-48}{2}=\frac{54}{2}= \boxed{27~cm}\\\\ AN = 102-27 = \boxed{75~cm} \\\\ \text{In triunghiurile: }\Delta CND \text{ si } \Delta DAN \text{ avem:}\\\\ \sphericalangle DCN = \sphericalangle NDA = 90°\\\\ \sphericalangle CDN = \sphericalangle DNA ~~\text{(alterne interne)}\\\\ \Longrightarrow~~\text{Cazul UU de asemanare}\\\\ \text{Scriem rapoartele de asemanare:}[/tex]


[tex]\displaystyle\\ \frac{DC}{ND} = \frac{ND}{AN}\\\\ ND^2 = AN\times DC = 75 \times 48 = 3600\\\\ ND = \sqrt{3600} = \boxed{60~cm} \\\\ \text{Pe NC il calculam cu T.P. din }\Delta CDN.\\\\ NC= \sqrt{ND^2-CD^2}= \sqrt{60^2-48^2}= \\\\ =\sqrt{3600-2304}=\sqrt{3600-2304}=\sqrt{1296}=\boxed{36~cm}\\\\ \text{Pe BC il calculam cu T.P. din }\Delta NBC.\\\\ BC = \sqrt{NB^2 + NC^2} = \sqrt{27^2 + 36^2} =\\\\ =\sqrt{729 + 1296} =\sqrt{2025} = \boxed{45~cm}[/tex]