The three different face diagonals of a cuboid (rectangular parallelopiped) have lengths 39, 40, 41.The length of the main diagonal of the cuboid which joins a pair of opposite corners :

Options

A. 49
B. `49sqrt(2)`
C. 60
D. `60sqrt(2)`

Answer

A

Explanation

`sqrt(a^(2)+b^(2))=39 `...(i)
`sqrt(b^(2)+c^(2))=40` ...(ii)
`sqrt(c^(2)+a^(2))=41` ....(iii)
`sqrt(a^(2)+b^(2)+c^(2))=?`
square and add (i), (ii) & (iii)
`2(a^(2)+b^(2)+c^(2))=39^(2)+40^(2)+41^(2)=4802`
`a^(2)+b^(2)+c^(2)=2401 rArr sqrt(a^(2)+b^(2)+c^(2))=49`