A cuboidal room has its length, breadth and height as a, b and c units respectively and if a + b + c = 25 units, ab + bc + ca = 240.5 units, then let us write the length of the longest rod that can be kept in this room

\mathrm{ (a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a) }

or, \mathrm{ (25)^2=a^2+b^2+c^2+2.240 .5 }

or, \mathrm{ 625=a^2+b^2+c^2+481 }

\therefore \mathrm{ a^2+b^2+c^2=625-481=144 }

\therefore The diagonal of the room \mathrm{ =\sqrt{a^2+b^2+c^2} }

\mathrm{ =\sqrt{144} } 12 m

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