# 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? [Hint: If x is the length of the shortest board, then (x + 3) and 2x are the length of the second and third piece, respectively. Thus x = (x + 3) + 2x ≤ 91 and 2x ≥ (x + 3) + 5]

**Solution:**

Let the length of the shortest piece in cm be x.

Then, the length of second and third piece in cm are (x + 3) and 2x respectively.

Since the three lengths are to be cut from a single piece of board of length 91 cm.

x + (x + 3) + 2x ≤ 91

⇒ 4x + 3 ≤ 91

⇒ 4x ≤ 91 - 3

⇒ 4x ≤ 88

⇒ x ≤ 88/4

⇒ x ≤ 22 .... (1)

Also, the third piece is at least 5 cm longer than the second piece

2x ≥ (x + 3) + 5

⇒ 2x ≥ x + 8

⇒ 2x - x ≥ 8

⇒ x ≥ 8 ....(2)

From (1) and (2), we obtain

8 ≤ x ≤ 22

Thus, the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 26

## 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? [Hint: If x is the length of the shortest board, then (x + 3) and 2x are the length of the second and third piece, respectively. Thus x = (x + 3) + 2x ≤ 91 and 2x ≥ (x + 3) + 5]

**Summary:**

A linear inequation x + (x + 3) + 2x ≤ 91 can be formed. We have found that the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm

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