Q. A man wants to cut three lengths from a single piece of board of length . The second length is to be longer than the shortest and the third length is to be twice as long as the shortest. The possible length of the shortest board, if the third piece is to be atleast longer than the second, is

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Solution:

Let the shortest side be .
Then, by given condition, second length
Third length
Also given, total length
Hence, sum of all the three lengths should be less than equal to 91 .


Subtracting to each term,





Third length second length
Again, given that

Transferring the term to LHS,

From Eqs. (i) and (ii), length of shortest board should be greater than or equal to 8 but less than or equal to 22 i.e.,