Question

trapezul dreptunghic ABCD de baze AB//CD , AB>CD , m (Â)=90° , are AD=12 cm , CD=9 cm si aria de 144cm2 Calculati a)lungimea diagonalei AC a trapezului b) perimetrul trapezului

Answer 1

a)AC^2 = DC^2 + AD^2 = 12^2 + 9^2 = 144 + 91 = 225
  AC = rad225 = 15
b) Aria trapez = (DC + AB)*AD/2 = 144 => (9+AB)*12 = 2*144
 9+AB = 2*12 = 24  => AB = 24 - 9 = 15
 Ducem CE perpend. pe AB => CE = AD  = 12
AE^2 = AC^2 - CE^2 = 15^2 - 12^2 = 225 - 81 = 81
AE = rad81 = 9  =>  BE = 15 - 9 =6
BC^2  = CE^2 + BE^2 = 12^2 + 6^2 = 144 + 36 = 180 = 4*9*5
BC = rad180 = 2*3*rad5 = 6rad5
Perim = 9 + 12 + 15 + 6rad5 = 36 + 6rad5 = 6(6 + rad5)