Odpowiedzi

2009-12-15T23:10:29+01:00
Obwód rombu = 16 cm
stosunek długości przekątnych tego rombu = 2/3
4a = 16 cm
a = 16 cm :4 = 4 cm
d1/d2 = 2/3
2d2 = 3d1 ---> d2 = (3/2)d1
(d1/2)² +(d2/2)² = a²
(d1)²/4 +[ (3/4)d1]² = a²
(d1)²/4 + (9/16) (d1)² = a² , mnożymy 16
4(d1)² + 9(d1)² = 16*a²
13(d1)² = 16 *16
(d1)² = [16*16]/13
d1 = 16/(√13)
d2 = (3/2)d1 = (3/2)*16/(√13)= 24/(√13)
P = [d1*d2]/2 = [16/(√13)*24/(√13)]/2 = [16*24]/[13*2] =
= [16*24]/26 = [16*12]/13 = 192/13
P = 192/13 cm²
P ≈ 14,77 cm²