Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area: 25a2−35a+12
(ii) Area: 35y2+13y−12
(i)Area of Rectangle =25a2−35a+12
We know that Area of Rectangle = length × breadth
So, we need to factorize the given polynomial to find length and breadth.
25a2−35a+12
= 25a2−20a−15a+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+13y−12
We know that Area of Rectangle = length × breadth
So, we need to factorize the given polynomial to find length and breadth.
35y2+13y−12
= 35y2+28y−15y−12
=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)