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NCERT Solutions for Class 9 Mathematics Chapter 14 Statistics
  • NCERT Solution For Class 9 Mathematics

    Statistics Here is the CBSE Mathematics Chapter 14 for Class 9 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 9 Mathematics Statistics Chapter 14 NCERT Solutions for Class 9 Mathematics Statistics Chapter 14 The following is a summary in Hindi and English for the academic year 2023-24. You can save these solutions to your computer or use the Class 9 Mathematics.

    Question 1
    CBSEENMA9003243

    A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

    Solution

    'a'   =  a
    'b'   =  a
    'c'   =  a
    therefore space space space space space space space space straight s space equals space fraction numerator apostrophe straight a apostrophe plus apostrophe straight b apostrophe plus apostrophe straight c apostrophe over denominator 2 end fraction equals fraction numerator straight a plus straight a plus straight a plus over denominator 2 end fraction equals fraction numerator 3 straight a over denominator 2 end fraction
    Area of the signal board
    equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root
equals square root of fraction numerator 3 straight a over denominator 2 end fraction open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses end root
square root of fraction numerator 3 straight a over denominator 2 end fraction open parentheses straight a over 2 close parentheses open parentheses straight a over 2 close parentheses open parentheses straight a over 2 close parentheses end root equals square root of fraction numerator 3 straight a to the power of 4 over denominator 16 end fraction end root equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared
    Perimeter = 180 cm
    rightwards double arrow   'a' + 'b' + 'c' = 180
    rightwards double arrow   a + a + a = 180
    rightwards double arrow              3a = 180
    rightwards double arrow space space space space space space space straight a space equals space 180 over 3
    rightwards double arrow space space space    a = 60  cm
    therefore  Area of the signal board equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared
               equals fraction numerator square root of 3 over denominator 4 end fraction left parenthesis 60 right parenthesis squared equals 900 square root of 3 space cm squared
    Alternatively,
         space space space space space straight s space equals fraction numerator 3 straight a over denominator 2 end fraction equals 3 over 2 left parenthesis 60 right parenthesis equals 90 space cm
    Area of the signal board
        equals square root of straight s left parenthesis straight s minus straight a left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root
equals square root of 90 left parenthesis 90 minus 60 right parenthesis left parenthesis 90 minus 60 right parenthesis left parenthesis 90 minus 60 right parenthesis end root
equals space square root of 90 left parenthesis 30 right parenthesis left parenthesis 30 right parenthesis left parenthesis 30 right parenthesis end root equals 900 square root of 3 space cm squared