A man wants to cut three lengths from a single piece of board of length \[91\]cm. The second length is to be \[3\]cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least \[5\]cm longer than the second? - Noon Academy

A man wants to cut three lengths from a single piece of board of length

$91$

cm. The second length is to be

$3$

cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least

$5$

cm longer than the second?

Class 11 | Exercise 6.1 | Linear Inequalities | Maths | NCERT

A man wants to cut three lengths from a single piece of board of length

$91$

cm. The second length is to be

$3$

cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least

$5$

cm longer than the second?

Solution:

Let us consider the length of the shortest piece be x cm

From the question, length of the second piece =

$(x+3)$

cm

Given, length of third piece is to be twice as long as the shortest =

$2x$

cm

Given that all the three lengths are to be cut from a single piece of board having a length of

$91$

cm

i.e.,

$x+(x+3)+2x\le 91$

cm

=

$4x+3\le 91$

=

$4x\le 88$

=

$4x/4\le 88/4$

=

$x\le 22$

… (i)

According to the question it is given that, the third piece is at least

$5$

cm longer than the second piece

i.e.,

$2x\ge (x+3)+5$

$2x\ge x+8$

$x\ge 8$

… (ii)

Now, from equation (i) and (ii) we have:

$8\le x\le 22$

Therefore, the length of the shortest board is greater than or equal to

$8$

cm and less than or equal to

$22$

cm

i

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