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Question

In front of a school are several gardens in rectangular raised beds. For the area of a rectangular garden .given, use factoring to find the possible dimensions. Could the garden be a perfect square? If so, explain why.
x squared minus 20 x plus 100

hintHint:

factorize the given area using a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared and find the possible values of length and breadth of the rectangle .Also judge if it is a square or not

The correct answer is: x-10 and x-10 are possible dimensions of the garden. yes,the garden is a perfect square as length and breadth are equal.


    Ans:- x - 10 and x - 10 are possible dimensions of the garden. yes, the garden is a perfect square as length and breadth are equal.
    Given, A equals x squared minus 20 x plus 100
    Write 20 x text  as  end text 2 left parenthesis 10 right parenthesis x text  and  end text 100 text  as  end text left parenthesis 10 right parenthesis squared text  then we get  end text x squared minus 2 left parenthesis 10 right parenthesis x plus 10 squared
    As a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared
    Here a = x ; b = 10
    We get A equals x squared minus 20 x plus 100 equals left parenthesis x minus 10 right parenthesis squared equals left parenthesis x minus 10 right parenthesis left parenthesis x minus 10 right parenthesis
    As the garden is rectangular , we can write area A =  length × breadth
    The only possibility is length = x-10 and breadth = x-10
    As length = breadth = x-10 the garden is a perfect square .

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