Cuboid - volume and areas

The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?

Correct result:

b =  10 cm
c =  5 cm

Solution:

V=250 cm3 S=250 cm2 a=5 m V=abc S=2(ab+bc+ac) 50=bc 125=5b+bc+5c c=50/b 125=5b+50+5⋅ 50/b 125b=5b2+50b+5∗50  125b=5b2+50b+5⋅ 50 −5b2+75b−250=0 5b2−75b+250=0  p=5;q=−75;r=250 D=q2−4pr=752−4⋅5⋅250=625 D>0  b1,2=−q±D2p=75±62510 b1,2=75±2510 b1,2=7.5±2.5 b1=10 b2=5   Factored form of the equation:  5(b−10)(b−5)=0  b=b1=10=10 cm

Our quadratic equation calculator calculates it.

c=b2=5=5 cm

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