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Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ x 21 2 x 10.5 ...... 2 x From (1) and (2), we obtain 5 10.5 . Since x is an even number, x can take the values, 6, 8 and 10. 6,8 , 8,10 Thus, the required possible pairs are 10,12 and . Question 25: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side. Solution 25: Let the length of the shortest side of the triangle be x cm. Then, length of the longest side = 3x cm Length of the third side 3x 2 cm Since the perimeter of the triangle is at least 61 cm, x cm 3x cm 3x 2 cm 61cm 7x 2 61 7x 61 2 7x 63 7x 63 7 7 x 9 Thus, the minimum length of the shortest side is 9 cm. 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: It x is the length of the shortest board, then x x 3 and third piece, respectively. Thu, x x 3 2x 91 and x x and 2x are the lengths of the second 2 3 5] Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.
Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ Solution 26: Let the length of the shortest piece be x cm. Then, length of the second piece and the third piece are (x + 3) cm and 2x cm respectively. Since the three lengths are to be cut from a single piece of board of length 91 cm, x cm x 3 cm 2x cm 91cm 4x 3 91 4x 91 3 4x 88 4x 88 4 4 x 22..... 1 Also, the third piece is at least 5 cm longer than the second piece. 2x x 3 5 2x x8 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. Exercise 6.2 Question 1: Solve the given inequality graphically in two-dimensional plane: Solution 1: The graphical representation of x y 5 This line divides the xy plane in two half planes, I and II. x y5 is given as dotted line in the figure below. Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, , which is true 0 0 5 or 0 5 Therefore, half plane II is not the solution region of the given inequality. Also, it is evident that any point on the line does not satisfy the given strict inequality. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.
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Class XI Chapter 1 - Sets Maths ___
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Class XI Chapter 2 - Relations and
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Class XI Chapter 3 - Trigonometric
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Class XI Chapter 4 - Principle of M
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 10 - Straight Line
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Class XI Chapter 12 - Introduction
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Class XI Chapter 13 - Limits and De
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Class XI Chapter 14 - Mathematical
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Class XI Chapter 15 - Statistics Ma
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