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Question

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area: 25a235a+12
(ii) Area: 35y2+13y12

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Solution

(i)Area of Rectangle =25a235a+12

We know that Area of Rectangle = length × breadth

So, we need to factorize the given polynomial to find length and breadth.

25a235a+12

= 25a220a15a+12

=5a(5a−4)−3(5a−4)

=(5a−4)(5a−3)

Therefore, Length=(5a−4) and Breadth=(5a−3) (1st possibility)

Or, Length =(5a−3) and Breadth =(5a−4) (2nd possibility)

(ii) Area of Rectangle = 35y2+13y12

We know that Area of Rectangle = length × breadth

So, we need to factorize the given polynomial to find length and breadth.

35y2+13y12

= 35y2+28y15y12

=7y(5y+4)−3(5y+4)

=(5y+4)(7y−3)

Therefore, Length=(5y+4) and Breadth=(7y−3) (1st possibility)

Or, Length =(7y−3) and Breadth =(5y+4) (2nd possibility)


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