The sum of length, breadth and height of a cuboid is 21c.m. and its diagonal is

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First , if you had worked it out, then should nothave asked it , and even if , somewhat helpful would not hadbeen a bad option either. For, the volume one, I really tried hard, but could not doit. But, in fact I think there may not be a unique answer. First, to get the volume, we need three equations, we haveonly two. We have : The sum = 21 and the sum of the squares = 196 . For example, if we know the sum of the cubes , then we wouldbe able to find the volume. I will also try to show that there might be infinitesolutions to the volume : suppose height, h = 81 = 9 Then ,   l2 + b2 +h2 = 196 or, l2 + b2 + 81 = 196 or, l2 + b2     = 115 ....(i)          and,      l + b + h =21    or,      l + b + 9 = 21    or,      l + b   = 12 ....(ii)    =>    l2 + b2 + 2lb = 144           or,    115 + 2lb = 144    .....using (i)    => lb =14.5      =>           l˜ 10.64 and b ˜ 1.36    using (ii)   =>          lbh = 130.5 cm3 now, let height, h= 100 = 10 Then ,   l2 + b2 +h2 = 196 or, l2 + b2 + 100 = 196 or, l2 + b2     = 96 ....(iii)          and,      l + b + h =21    or,      l + b + 10 = 21    or,      l + b   = 11 ....(iv)    =>    l2 + b2 + 2lb = 121           or,    96 + 2lb = 121    .....using (iii)    => lb =12.5      =>           l˜ 9.71 and b ˜ 1.29    using (iv)   =>          lbh = 125 cm3 So, I have two distinct set of solutions with the same givenproperties. ( 9.71 , 1.29, 10 ) and (10.64 , 1.36 , 9 )

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