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Maths-

General

Easy

Question

The area of a playground is $36 x squared minus 16 y squared$ . Without removing common factors, factor to possible dimensions of the playground. How are the side-lengths related? What value would you need to subtract from the longer side and add to the shorter side for the playground to be a square?

hint Hint:

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 .Find the value that is needed to subtract from the longer side and add to the shorter side for the rug to be a square.

The correct answer is: 6x+4y and 6x-4y are the dimensions of a rectangular playground . 4y needs to be subtracted from the longer side(6x+4y) and adding it to the shorter side(6x-4y) gives the playground to be a square

Ans :- 6x + 4y and 6x - 4y are the dimensions of a rectangular playground . 4y needs to be subtracted from the longer side(6x + 4y) and adding it to the shorter side(6x - 4y) gives the playground to be a square .
Given, $A equals 36 x squared minus 16 y squared$
Write $16 y squared text as end text left parenthesis 4 y right parenthesis squared text and end text 36 x squared text as end text left parenthesis 6 x right parenthesis squared text then we get end text left parenthesis 6 x right parenthesis squared minus left parenthesis 4 y right parenthesis squared$
As $a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis$
Here $a equals 6 x semicolon b equals 4 y$
We get $A equals 36 x squared minus 16 y squared equals left parenthesis 6 x plus 4 y right parenthesis left parenthesis 6 x minus 4 y right parenthesis$
As the garden is rectangular , we can write area A = length × breadth
The possibility is length = 6x + 4y and breadth = 6x - 4y (or) viceversa
4y needs to be subtracted from the longer side(6x + 4y) and adding it to the shorter side(6x - 4y) gives the playground to be a square

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