Maths-
General
Easy

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
A equals x squared plus 32 x plus 256

hintHint:

 factorize the given area using a squared plus 2 a b plus b squared equals left parenthesis a plus 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+16 and x+16 are possible dimensions of the garden. yes,the garden is a perfect square as length and breadth are equal.


    Ans:- x + 16 and x + 16 are possible dimensions of the garden. yes,the garden is a perfect square as length and breadth are equal.
    Given, A equals x squared plus 32 x plus 256
    Write 32 x text  as  end text 2 left parenthesis 16 right parenthesis x text  and  end text 256 text  as  end text left parenthesis 16 right parenthesis squared text  then we get  end text x squared plus 2 left parenthesis 16 right parenthesis x plus 16 squared
    As a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared
    Here a = x ; b = 16
    We get A equals x squared plus 32 x plus 256 equals left parenthesis x plus 16 right parenthesis squared equals left parenthesis x plus 16 right parenthesis left parenthesis x plus 16 right parenthesis
    As the garden is rectangular , we can write area A =  length × breadth
    The only possibility is length = x + 16 and breadth = x + 16
    As length = breadth = x + 16 the garden is a perfect square .

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