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 minus 4 y squared

hintHint:

factorize the given area using a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis 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-2y and x+2y are possible dimensions of the garden. No,the garden is not a perfect square as length and breadth are not equal.


    Ans:- x - 2y and x + 2y are possible dimensions of the garden. No,the garden is not a perfect square as length and breadth are not equal.
    Given, A equals x squared minus 4 y squared
    Write 4 y squared text  as  end text left parenthesis 2 y right parenthesis squared text  then we get  end text x squared minus left parenthesis 2 y right parenthesis squared
    As a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis
    Here a = x ; b = 2y
    We get A equals x squared minus 4 y squared equals left parenthesis x plus 2 y right parenthesis left parenthesis x minus 2 y right parenthesis
    As the garden is rectangular , we can write area A =  length × breadth
    The possibility is length = x + 2y and breadth = x - 2y (or) viceversa
    As length  breadth the garden is not a perfect square

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