Three altitudes

A triangle with altitudes 4; 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.

Correct answer:

a =  7.5236 cm
b =  6.0189 cm
c =  5.0157 cm
t1 =  4.0671 cm
t2 =  5.6413 cm
t3 =  6.3345 cm

Step-by-step explanation:

v1=4 cm v2=5 cm v3=6 cm  h=21/v1+1/v2+1/v3=21/4+1/5+1/6=120370.3083 t=h (h1/v1) (h1/v2) (h1/v3)=0.3083 (0.30831/4) (0.30831/5) (0.30831/6)0.0003  s=4 t=4 0.00030.0665 S=s1=0.0665115.0472 cm2  S=2a v1  a=2 S/v1=2 15.0472/4=7.5236 cm

Try calculation via our triangle calculator.

b=v22 S=52 15.0472=6.0189 cm
c=v32 S=62 15.0472=5.0157 cm
t1=22 b2+2 c2a2=22 6.01892+2 5.015727.52362=4.0671 cm
t2=22 a2+2 c2b2=22 7.52362+2 5.015726.01892=5.6413 cm
t3=22 a2+2 b2c2=22 7.52362+2 6.018925.01572=6.3345 cm

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