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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 :A. 49B. `49sqrt(2)`C. 60D. `60sqrt(2)` |
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Answer» Correct Answer - A `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` |
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