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 answer:

b =  30 cm
c =  5 cm

Step-by-step explanation:

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 =  c2 22500 + 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=2ab±D=2925±765625 x1,2=2925±875 x1,2=462.5±437.5 x1=900 x2=25  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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