Question

va rog mult aflati  raza cercului inscris in triunghiul ABC care are laturile AB=14 cm
BC=16 cm sc CA=18 cm

Answer 1

r=S/p

S=√p(p-a)(p-b)(p-c)

p=(a+b+c)/2=  (14+16+18)/2=48/2= 24

S=√24(24-16)(24-14)(24-18)
=√2³*3 * 8 * 10 * 6=
=√2³ * 3 * 2³ * 2*5* 2*3=
=2³*2*3√5
=16*3√5
=48√5

r=48√5/24=  2√5

Answer 2

$r=\dfrac Sp,\ \ unde \ \ p=\dfrac{a+b+c}{2};\ \ S=\sqrt{p(p-a)(p-b)(p-c)}$

$p=\dfrac{14+16+18}{2}=24\ cm$

$S=\sqrt{24\cdot10\cdot8\cdot6}=\sqrt{24^2\cdot20}=48\sqrt5\ cm^2$

$r=\dfrac{48\sqrt5}{24}=2\sqrt5\ cm$