SSC CPO SI and ASI 2011 Paper

Question : 129 of 200

Marks: +1, -0

If the sum of three dimensions and the total surface area of a rectangular box are 12 cm

^{2}

and 94 cm

^{2}

, respectively, then the maximum length of a stick that can be placed inside the box is

Solution:

(1) Let the length, breadth and height of the box be p cm, q cm and r cm, respectively. Now, the maximum length of the stick will be,

√{ {p}^{2}+ {q}^{2}+ {r}^{2}}

=√{( {p}+ {q}+ {r})^{2}-2( {pq}+ {qr}+ {rp})}

=√{( { \sum \of \three \dimensions })^{2} -(\total \surface \area)}

=√{144-94}=√{50}=5 √{2} {cm}

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