a=najkrótszy bok b= średni bok=a+3,5cm c=najdłuzszy bok c/b=13/12 12c=13b b=12c/13 a/b=5/12 a/(a+3,5)=5/12 12a=5a+17,5 12a-5a=17,5 a=17,5:7 a=2,5cm ............. b=a+3,5=2,5+3,5=6cm 12c=13b c=13b/12=13×6:12=6,5 to trójkat prostokatny bo; 2,5²+6²=6,5² 42,25=42,25 obwód=2,5+6+6,5=15cm p=½ab=½×2,5×6=7,5cm²
c = 13 x b = 12 x a = 5 x Mamy b = a + 3,5 zatem a^2 + b^2 = c^2 a^2 + ( a + 3,5)^2 = c^2 ( 5x)^2 + ( 5x + 3,5)^2 = (13x)^2 25x^2 + 25 x^2 + 35x + 12,25 = 169 x^2 119 x^2 - 35 x - 12,25 = 0 --------------------------------- delta = (-35)^2 - 4*119*(- 12,25) = 1225 + 5 831 = 7 056 p(delty) = 84 zatem x = [ 35 + 84]/238 = 119/238 = 1/2 lub x = [ 35 - 84]/238 < 0 - odpada Mamy zatem c = 13 x= 13*0,5 = 6,5 b = 12 x = 12*0,5 = 6 a = 5 x = 5*0,5 = 2, 5 mamy więc a = 2,5 cm; b = 6 cm; c = 6,5 cm Pole trójkąta P =0,5 a*b = 0,5*2,5 cm * 6 cm = 7,5 cm^2 ====================================== Obwód L =a + b + c = [ 2,5 + 6 + 6,5 ] cm = 15 cm =========================================
