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 result:

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

Solution:

v1=4 cm v2=5 cm v3=6 cm  h=1/v1+1/v2+1/v32=1/4+1/5+1/62=371200.3083 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=1s=10.066515.0472 cm2  S=a v12  a=2 S/v1=2 15.0472/4=7.5236 cm

Try calculation via our triangle calculator.

b=2 Sv2=2 15.04725=6.0189 cm
c=2 Sv3=2 15.04726=5.0157 cm
t1=2 b2+2 c2a22=2 6.01892+2 5.015727.523622=4.0671 cm
t2=2 a2+2 c2b22=2 7.52362+2 5.015726.018922=5.6413 cm
t3=2 a2+2 b2c22=2 7.52362+2 6.018925.015722=6.3345 cm



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