NCERT Solutions for Class 9 Maths Chapter 9 Exercise 9.2 Solutions

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NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Exercise 9.2 Solutions are based on parallelograms with the same base and parallel lines.

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Exercise Solutions of Class 9 Maths Chapter 9 Areas Of Parallelograms And Triangles 

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CBSE X Related Questions

1.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos2 A – sinA or not

      2.
      Find the sums given below :
      1. \(7 + 10\frac 12+ 14 + ....... + 84\)
      2. \(34 + 32 + 30 + ....... + 10\)
      3. \(–5 + (–8) + (–11) + ....... + (–230)\)

          3.

          Form the pair of linear equations for the following problems and find their solution by substitution method.

          (i) The difference between two numbers is 26 and one number is three times the other. Find them.

          (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

          (iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

          (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km.

          (v) A fraction becomes\(\frac{ 9}{11}\), if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes \(\frac{5}{6}\). Find the fraction.

          (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

              4.

              Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

                  5.

                  The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :

                  Length (in mm)

                  Number of leaves

                  118 - 126

                  3

                  127 - 135 

                  5

                  136 - 144

                  9

                  145 - 153

                  12

                  154 - 162

                  5

                  163 - 171

                  4

                  172 - 180

                  2

                  Find the median length of the leaves. 
                  (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

                      6.

                      Solve the following pair of linear equations by the substitution method. 
                      (i) x + y = 14 
                          x – y = 4   

                      (ii) s – t = 3 
                          \(\frac{s}{3} + \frac{t}{2}\) =6 

                      (iii) 3x – y = 3 
                            9x – 3y = 9

                      (iv) 0.2x + 0.3y = 1.3 
                           0.4x + 0.5y = 2.3 

                      (v)\(\sqrt2x\) + \(\sqrt3y\)=0
                          \(\sqrt3x\) - \(\sqrt8y\) = 0

                      (vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
                          \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

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