Cuboid

Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.

Correct result:

b =  30 cm
c =  5 cm

Solution:

a=6 cm V=900 cm3 u=31 cm  V=abc 900=6 bc bc=150  u=a2+b2+c2  312=62+b2+c2  925=b2+c2 925=22500c2+c2 c4925 c2+22500=0 x=c2  x2925x+22500=0  x2925x+22500=0  a=1;b=925;c=22500 D=b24ac=92524122500=765625 D>0  x1,2=b±D2a=925±7656252 x1,2=925±8752 x1,2=462.5±437.5 x1=900 x2=25   Factored form of the equation:  (x900)(x25)=0  c1=x1=900=30 c2=x2=25=5  b=c1=30=30 cm

Our quadratic equation calculator calculates it.

c=c2=5=5 cm   Verifying Solution:  d=a2+b2+c2=62+302+52=31 d=u V2=a b c=6 30 5=900 cm3 V2=V



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